Black hole

From Wikipedia, the free encyclopedia

This article or section is in need of attention from an expert on the subject. Please help recruit one or improve this article yourself. See the talk page for details. Please consider using {{Expert-subject}} to associate this request with a WikiProject

This article may require cleanup to meet Wikipedia's quality standards. Please discuss this issue on the talk page or replace this tag with a more specific message. This article has been tagged since March 2007.

General Relativity

General relativity

Introduction to... Mathematical formulation of...

Fundamental concepts

Special relativity · Equivalence principle World line · Riemannian geometry

Phenomena

Black hole · Event horizon · Lenses Waves · Singularity Frame-dragging

Equations

Linearized Gravity Einstein field equations

Advanced theories

Kaluza-Klein Quantum gravity

Solutions

Schwarzschild · Kasner · Kerr Milne · Reissner-Nordström Robertson-Walker

Scientists

Einstein · Minkowski · Eddington Lemaître · Schwarzschild Robertson · Kerr · Friedman Chandrasekhar · Hawking · others

This box: view • talk • edit

A black hole is an object with a gravitational field so powerful that even electromagnetic radiation (such as light) cannot escape its pull.^[1]

Both Newtonian physics and Einstein's general relativity predict the existence of black holes, but general relativity provides a much more accurate and informative analysis, for example:

• The Newtonian version incorrectly assumes that photons have rest mass (see History of the black hole concept).
• The Newtonian version is based on the concept of escape velocity and therefore cannot explain: why there is a well-defined region from which nothing can escape; why the most powerful spaceship cannot escape.

Merely having a very large mass is not enough to make a black hole - if it were, most galaxies would be black holes. A black hole consists of mass concentrated into an abnormally small volume:

• The gravitational pull between two objects is inversely proportional to the square of the distance between them (Newton's Law of Gravitation). For example, if you reduce the distance by a factor of 10 you increase the force by a factor of 100. So a star's or planet's gravitational pull becomes stronger very rapidly as the distance from its center decreases.
• In a normal star or even in a neutron star the radius of the outer surface is so large that the gravitational pull at the surface is not strong enough to prevent light from escaping.
• So a black hole can only form if a similar mass is compressed into a much smaller radius - so small that the result is not like anything one could reasonably describe as "matter".

[edit] Sizes of black holes

Black holes can be of any mass. Since gravity increases in strength as volume is decreased, any object sufficiently compressed will become a black hole. However in nature where black holes form naturally only black holes of a few mass ranges are common.

Black holes can be divided into several size categories:

• Supermassive black holes containing millions to billions of solar masses are believed to exist in the center of most galaxies, including our own Milky Way.
  Note: 1 solar mass = the mass of our sun.
• Intermediate-mass black holes, whose size is measured in thousands of solar masses. Intermediate-mass black holes have been proposed as a possible power source for ultra-luminous X ray sources.
• Stellar-mass black holes have masses ranging from 1.44 to 15 solar masses. This is narrower than the range of masses found in "normal" stars because of the way in which black holes are formed: the smallest star which is large enough to produce a black hole will form a black hole of 1.44 solar masses (the Chandrasekhar limit); large stars usually blow away a significant percentage of their mass in supernovae as part of the process that forms black holes.
• Mini black holes, small black holes which are smaller than stellar-mass black holes but larger than micro black holes(not theorized to exist, due to the absence of a suitable formation method).
• Micro black holes, which have masses similar to that of a helium atom.Also known as primordial black holes.

Astrophysicists expect to find stellar-mass and larger black holes, because a stellar mass black hole is formed by the gravitational collapse of a star of 3 or more solar masses at the end of its "normal" lifetime, and can then act as a "seed" for the formation of a much larger black hole.

Micro black holes may theoretically be produced by:

• The Big Bang, which produced pressures far larger than that of a supernova and therefore sufficient to produce primordial black holes without needing the powerful gravity fields of collapsing large stars.
• High-energy particle accelerators such as the Large Hadron Collider (LHC), if certain non-standard assumptions are correct (typically, an assumption of large extra dimensions). However, any black holes produced in such a manner will evaporate practically instantaneously, thus posing no danger to earth.

There is a gap in the size range - black holes which are larger than micro but smaller than stellar mass. Such black holes are too small to be produced by the collapse of stars and too large to be produced by any conceivable particle accelerator. Perhaps some primordial black holes are in this range, but that is mere speculation.

[edit] The mechanism of black holes

General relativity states that it is impossible to propel matter or energy past the speed of light, since the energy needed rises exponentially as one tries to do so, in a manner rather similar to a cubic graph. Any mass bends or warps space-time and creates a gravity field that is capable of attracting energy and matter. This therefore leads to the logical conclusion that it is possible that a region in spacetime can be so warped, or, in other words a region where gravity is so strong, that light cannot escape from it. Since light cannot escape, nothing can!

A black hole is the terminology for such an area, it contains enough mass in a small enough volume to bend space-time such that the speed needed to escape, or the escape velocity is greater than the speed of light. Since the strength of gravity decreases outward from the source of the gravity, there is a boundary outside of which the escape velocity is lower than the speed of light, and inside of which is greater. This is known as the event horizon and is the boundary of the black hole.

It therefore follows that anything that falls into a black hole is irretrievable, it cannot escape from the region, therefore the terminology.

Most black holes existing today are stars that have collapsed due to their own gravity. After the nuclear fusion in their core has stopped due to lack of fuel, the star undergoes a violent collapse known as a supernova. Due to the large mass of the star and the huge force of gravity acting on the star, there is no known force known today that can prevent this collapse. Electron degeneracy pressure and baryon degeneracy pressure are all insufficient to stop gravity from crushing the star. In layman's terms the forces that force matter to conform to the everyday law "matter occupies space" have been overcome. The star collapses completely and forms a structure known as a singularity, a point object with mass but zero volume, and infinite density. Since gravity is inversely proportional to the distance from the center of the object, the strength of gravity on the "surface" of the singularity is also infinite.

Even though black holes may resemble fundamental particles like quarks and electrons, their charge is greater than their mass, and, as the Reissner-Nordström metric predicts, do not have horizons.

[edit] Do black holes have "no hair"?

The "No hair" theorem states that black holes have only 3 independent internal properties: mass, angular momentum and electric charge. It is impossible to tell the difference between a black hole formed from a highly compressed mass of normal matter and one formed from, say, a highly compressed mass of anti-matter, in other words, any information about infalling matter or energy is destroyed.

[edit] Types of black holes

Despite the uncertainty about whether the "No Hair" theorem applies to our universe, astrophysicists currently classify black holes according to their angular momentum (non-zero angular momentum means the black hole is rotating) and electric charge:

(All black holes have non-zero mass, so mass cannot be used for this type of "yes / "no" classification)

Physicists do not expect that black holes with a significant electric charge will be formed in nature, because the electromagnetic repulsion which resists the compression of an electrically charged mass is about 40 orders of magnitude greater (about 10⁴⁰ times greater) than the gravitational attraction which compresses the mass. So this article does not cover charged black holes in detail, but the Reissner-Nordström black hole and Kerr-Newman metric articles provide more information.

On the other hand astrophysicists expect that almost all black holes will rotate, because the stars from which they are formed rotate. In fact most black holes are expected to spin very rapidly, because they retain most of the angular momentum of the stars from which they were formed but concentrated into a much smaller radius. The same laws of angular momentum make skaters spin faster if they pull their arms closer to their bodies.

This article describes non-rotating, uncharged black holes first, because they are the simplest type.

[edit] Major features of non-rotating, uncharged black holes

[edit] Event horizon

This is the boundary of the region from which not even light can escape. An observer at a safe distance would see a dull black sphere if the black hole was in a pure vacuum but in front of a light background such as a bright nebula. The event horizon is not a solid surface, and does not obstruct or slow down matter or radiation which is traveling towards the region within the event horizon.

The event horizon is the defining feature of a black hole - it is black because no light or other radiation can escape from inside it. So the event horizon hides whatever happens inside it and we can only calculate what happens by using the best theory available, which at present is general relativity.

The gravitational field outside the event horizon is identical to the field produced by any other spherically symmetric object ("perfect ball") of the same mass. The popular conception of black holes as "sucking" things in is false: objects can maintain an orbit around black holes indefinitely provided they stay outside the event horizon.

[edit] Singularity at a single point

A mathematical singularity is a situation in which a set of equations goes badly wrong. According to general relativity, a black hole's mass is entirely compressed into a region with zero volume, which means its density and gravitational pull are infinite, and so is the curvature of space-time which it causes. These infinite values cause most physical equations, including those of general relativity, to stop working at the center of a black hole. So physicists call the zero-volume, infinitely dense region at the center of a black hole a "singularity".

The singularity in a non-rotating, uncharged black hole is a point, in other words it has zero length, width and height.

But there is an important uncertainty about this description: quantum mechanics is as well-supported by mathematics and experimental evidence as general relativity, and does not allow objects to have zero size - so quantum mechanics says the center of a black hole is not a singularity but just a very large mass compressed into the smallest possible volume. At present we have no well-established theory which combines quantum mechanics and general relativity; and the most promising candidate, string theory, also does not allow objects to have zero size.

The rest of this article will follow the predictions of general relativity, because quantum mechanics deals with very small-scale (sub-atomic) phenomena and general relativity is the best theory we have at present for explaining large-scale phenomena such as the behavior of masses similar to or larger than stars.

[edit] A photon sphere

A non-rotating black hole's photon sphere is a spherical boundary of zero thickness such that photons moving along tangents to the sphere will be trapped in a circular orbit. For non-rotating black holes, the photon sphere has a radius 1.5 times larger than the radius of the event horizon. No photon is likely to stay in this orbit for long, for two reasons. First, it is likely to interact with any infalling matter in the vicinity (being absorbed or scattered). Second, the orbit is dynamically unstable; small deviations from a perfectly circular path will grow into larger deviations very quickly, causing the photon to either escape or fall into the hole.

Other extremely compact objects such as neutron stars can also have photon spheres.^[2] This follows from the fact that light "captured" by a photon sphere does not pass within the radius that would form the event horizon if the object were a black hole of the same mass, and therefore its behavior does not depend on the presence of an event horizon.

[edit] Accretion disk

Space is not a pure vacuum - even interstellar space contains a few atoms of hydrogen per cubic centimeter. The powerful gravity field of a black hole pulls this towards and then into the black hole. The gas nearest the event horizon forms a disk and, at this short range, the black hole's gravity is strong enough to compress the gas to a relatively high density. The pressure, friction and other mechanisms within the disk generate enormous energy - in fact they convert matter to energy more efficiently than the nuclear fusion processes that power stars. As a result, the disk glows very brightly, although disks around black holes radiate mainly X-rays rather than visible light.

Accretion disks are not proof of the presence of black holes, because other massive, ultra-dense objects such as neutron stars and white dwarfs cause accretion disks to form and to behave in the same ways as those round black holes.

[edit] Major features of rotating black holes

Main article: Rotating black hole

Two important surfaces around a rotating black hole. The inner sphere is the static limit (the event horizon). It is the inner boundary of a region called the ergosphere. The oval-shaped surface, touching the event horizon at the poles, is the outer boundary of the ergosphere. Within the ergosphere a particle is forced (dragging of space and time) to rotate and may gain energy at the cost of the rotational energy of the black hole (Penrose process).

Rotating black holes share many of the features of non-rotating black holes - inability of light or anything else to escape from within their event horizons, accretion disks, etc. But general relativity predicts that rapid rotation of a large mass produces further distortions of space-time in addition to those which a non-rotating large mass produces, and these additional effects make rotating black holes strikingly different from non-rotating ones.

[edit] Two event horizons

If two rotating black holes have the same mass but different rotation speeds, the inner event horizon of the faster-spinning black hole will have a larger radius and its outer event horizon will have a smaller radius than in the slower-spinning black hole. In the most extreme case the two event horizons have zero radius, the region hidden by them has zero size and therefore the object is not a black hole but a naked singularity. Many physicists think that some principle which has not yet been discovered prevents the existence of a naked singularity and therefore prevents a black hole from spinning fast enough to create one.

[edit] Two photon spheres

General relativity predicts that a rotating black hole has two photon spheres, one for each event horizon. A beam of light traveling in a direction opposite to the spin of the black hole will circularly orbit the hole at the outer photon sphere. A beam of light traveling in the same direction as the black hole's spin will circularly orbit at the inner photon sphere. This beam will then split itself in two. Both pieces will move into the Hole

[edit] Ergosphere

A large, ultra-dense rotating mass creates an effect called frame-dragging, so that space-time is dragged round it in the direction of the rotation. If you find that hard to imagine, think of a large fairground roundabout (but not a waltzer!) - from the point of view of a rider all the other riders appear to stay in the same places, but from a spectator's point of view all the riders are whirling round.

Rotating black holes have an ergosphere, a region bounded by:

• on the outside, an oblate spheroid which coincides with the event horizon at the poles and is noticeably wider round the "equator". This boundary is sometimes called the "ergosurface", but it is just a boundary and has no more solidity than the event horizon. At points exactly on the ergosurface, space-time is dragged round at the speed of light.
• on the inside, the outer event horizon.

Within the ergosphere space-time is dragged round faster than light - general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.

Objects and radiation (including light) can stay in orbit within the ergosphere without falling to the center. But they cannot hover (remain stationary as seen by an external observer) because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.

Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way the black hole will spin more slowly and may even stop spinning eventually.

[edit] Ring-shaped singularity

General relativity predicts that a rotating black hole will have a ring singularity which lies in the plane of the "equator" and has zero width and thickness - but remember that quantum mechanics does not allow objects to have zero size in any dimension, so general relativity's prediction is only the best idea we have until someone devises a theory which combines general relativity and quantum mechanics.

[edit] Possibility of escaping from a rotating black hole

Kerr's solution for the equations of general relativity predicts that:

• The properties of space-time between the two event horizons allow objects to move only towards the singularity.
• But the properties of space-time within the inner event horizon allow objects to move away from the singularity, pass through another set of inner and outer event horizons, and emerge out of the black hole into another universe or another part of this universe without traveling faster than the speed of light.

If this is true, rotating black holes could theoretically provide the wormholes which often appear in science fiction. Unfortunately, it is unlikely that the internal properties of a rotating black hole are exactly as described by Kerr's solution^[3] and it is not currently known whether the actual properties of a rotating black hole would provide a similar escape route for an object via the inner event horizon.

Even if this escape route is possible, it is unlikely to be useful because a spacecraft which followed that path would probably be distorted beyond recognition by spaghettification.

[edit] What happens when something falls into a black hole

This section describes what happens when something falls into a non-rotating, uncharged black hole. The effects of rotating and charged black holes are more complicated but the final result is much the same - the falling object is absorbed (unless rotating black holes really can act as wormholes).

[edit] Spaghettification

An object in any very strong gravity field is spaghettified (stretched like spaghetti), because:

• The inverse square law means that there is a stronger gravitational pull on the side of the object nearest the source of the gravity field than on the far side.
• In an extremely strong gravity field, the difference in pull is great enough to stretch the object.

An object does not need be falling to be spaghettified - it can happen to objects which are orbiting in or even moving out of a very strong gravity field. But spaghettification becomes increasingly intense for falling objects because: the gravity field is stronger closer to its source; the distance between the object's leading and trailing sides becomes a larger fraction of the total distance from the object to the gravity source.

Strictly speaking an object should only be spaghettified if it is not tumbling. If it's tumbling, the result should be more like what happens when pizza dough is being made.

A relatively low-mass black hole will start to spaghettify a falling object before the object reaches the event horizon, while a super-massive black hole will not cause noticeable spaghettification. Now scientists think you'd be 'roasted' in a black hole.^[4] That's one of several surprises that the inverse square law produces when you apply it to black holes (another is that, if you define a black hole's density as its mass divided by the volume of the region inside the event horizon, low-mass black holes are denser than high-mass ones).

[edit] Before the falling object crosses the event horizon

An object in a gravitational field experiences a slowing down of time, called time dilation, relative to an observers outside the field - the observer will see that physical processes in the object, including clocks, appear to run slowly. Near the event horizon, the time dilation increases rapidly.

From the viewpoint of a distant observer, an object falling into a black hole appears to slow down, approaching but never quite reaching the event horizon: and it appears to become redder and dimmer, because of the extreme gravitational red shift caused by the gravity of the black hole. Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon. All of this is a consequence of time dilation: the object's movement is one of the processes that appear to run slower and slower, and the time dilation effect is more significant than the acceleration due to gravity; the frequency of light from the object appears to decrease, making it look redder, because the light appears to complete fewer cycles per "tick" of the observer's clock; lower-frequency light has less energy and therefore appears dimmer.

From the viewpoint of the falling object, distant objects may appear either blue-shifted or red-shifted, depending on the falling object's trajectory. Light is blue-shifted by the gravity of the black hole, but is red-shifted by the velocity of the falling object.

[edit] As the object passes through the event horizon

From the viewpoint of the falling object, nothing particularly special happens at the event horizon (apart from spaghettification, if the black hole has relatively low mass).

The curious thing is that, due to time dilation, an outside observer will never see an object cross this line - the object will instead fade from view as the frequency and photon emission rates are reduced. The net effect is that we can see nothing that occurs within the horizon, as all the light is caught in the gravity well.

[edit] Inside the event horizon

The object reaches the singularity at the center within a finite amount of proper time, as measured by a watch fixed to the falling object.

An observer on the falling object would continue to see objects outside the event horizon, blue-shifted or red-shifted depending on the falling object's trajectory (assuming that the observer survived spaghettification long enough to see anything). But the observer would not see anything closer than himself / herself / itself to the singularity, because the singularity bends space-time so that light can only travel towards the center. For example if the observer fell feet-first, his / her / its feet would be invisible.

[edit] Hitting the singularity

By this time any falling observer is dead or has ceased to work (if it's a machine) because of spaghettification.

In fact spaghettification increases in power at an incredible rate as the falling object approaches the singularity, so that:

• The object is torn into its component atoms.
• Then the electrons are stripped from the atoms.
• Then the nuclei are ripped apart, into protons and neutrons.
• Then the protons and neutrons are torn apart into quarks.
• Then ... we don't know what happens next (immediately before contact with the singularity), because electrons and quarks are the most fundamental particles known to physics at present. And these particles and whatever they might become next are so small that quantum mechanics governs their behavior as much as general relativity, but physicists have not yet found a theory which combines quantum mechanics and general relativity.
• Finally there is nothing left of the falling object, and the black hole has slightly greater mass.

[edit] Formation and evaporation

[edit] Formation of stellar-mass black holes

Stellar-mass black holes are formed in two ways:

• As a direct result of the gravitational collapse of a star.
• By collisions between neutron stars.^[5] Although neutron stars are fairly common, collisions appear to be very rare. Neutron stars are also formed by gravitational collapse, which is therefore ultimately responsible for all stellar-mass black holes.

Stars undergo gravitational collapse when they can no longer resist the pressure of their own gravity. This usually occurs either because a star has too little "fuel" left to maintain its temperature, or because a star which would have been stable receives a lot of extra matter in a way which does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight (Charles's law explains the connection between temperature and volume).

The collapse transforms the matter in the star's core into a denser state which forms one of the types of compact star. Which type of compact star is formed depends on the mass of the remnant, i.e. of the matter left to be compressed after the supernova (if one happened - see below) triggered by the collapse has blown away the outer layers.

Only the largest remnants, those exceeding 5 solar masses, generate enough pressure to produce black holes, because singularities are the most radically transformed state of matter known to physics (if you can still call it matter) and the force which resists this level of compression, neutron degeneracy pressure, is extremely strong. Remnants exceeding 5 solar masses are produced by stars which were over 20 solar masses before the collapse (the rest of the mass is usually blown into space by the supernova triggered by the collapse).

In stars which are too large to form white dwarfs, the collapse releases energy which usually produces a supernova, blowing the star's outer layers into space so that they form a spectacular nebula. But the supernova is a side-effect and does not directly contribute to producing a compact star. For example a few gamma ray bursts were expected to be followed by evidence of supernovae but this evidence did not appear,^[6][7] and one explanation is that some very large stars can form black holes fast enough to swallow the whole star before the supernova blast can reach the surface.

[edit] Formation of larger black holes

There are two main ways in which black holes of larger than stellar mass can be formed:

• Stellar-mass black holes may act as "seeds" which grow by absorbing mass from interstellar gas and dust, stars and planets or smaller black holes.
• Star clusters of large total mass may be merged into single bodies by their members' gravitational attraction. This will usually produce a supergiant or hypergiant star which runs short of "fuel" in a few million years and then undergoes gravitational collapse, produces a supernova or hypernova and spends the rest of its existence as a black hole.

[edit] Formation of smaller black holes

New black holes of less than stellar mass cannot be formed naturally in today's universe because the smallest mass which can collapse to form a black hole produces a stellar mass black hole of 1.44 solar masses.

But there are still a few ways in which smaller black holes might be formed:

• By evaporation of larger black holes. But this depends on the Hawking radiation theory, about which there are still some doubts, and in any case can only cause the smallest black holes to evaporate.
• By the Big Bang, which produced sufficient pressure to form smaller black holes without the need for anything resembling a star. These primordial black holes are at present just a hypothesis.
• By very powerful particle accelerators. According to the most widely-accepted theories, we would need particle accelerators several orders of magnitude more powerful than we can build at present in order to produce even a micro black hole.
  But some models of the unification of the four fundamental forces do allow the formation of micro black holes under laboratory conditions. These models postulate that the energy at which gravity is unified with the other forces is comparable to the energy at which the other three are unified, as opposed to being the Planck energy (which is much higher). This would allow production of extremely short-lived black holes in terrestrial particle accelerators. No conclusive evidence of this type of black hole production has been presented.

[edit] Evaporation

Hawking radiation is a theoretical process by which black holes can evaporate into nothing. As there is no experimental evidence to corroborate it and there are still some major questions about the theoretical basis of the process, there is still debate about whether Hawking radiation can make black holes evaporate.

Quantum mechanics says that even the purest vacuum is not completely empty but is instead a "sea" of energy which has wave-like flutuations. We cannot observe this "sea" of energy directly because there is no lower energy level with which we can compare it. The fluctuations in this sea produce pairs of particles in which one is made of normal matter and the other is the corresponding antiparticle (special relativity proves mass-energy equivalence, i.e. that mass can be converted into energy and vice versa). Normally each would soon meet another instance of its antiparticle and the two would be totally converted into energy, restoring the overall matter-energy balance as it was before the pair of particles was created. The Hawking radiation theory suggests that, if such a pair of particles is created just outside the event horizon of a black hole, one of the two particles may fall into the black hole while the other escapes, because the two particles move in slightly different directions after their creation. From the point of view of an outside observer, the black hole has just emitted a particle and therefore the black hole has lost a minute amount of its mass.

If the Hawking radiation theory is correct, only the very smallest black holes are likely to evaporate in this way. For example a black hole with the mass of our Moon would gain as much energy (and therefore mass - mass-energy equivalence again) from cosmic microwave background radiation as it emits by Hawking radiation, and larger black holes will gain more energy (and mass) than they emit. To put this in perspective, the smallest black hole which can be created naturally at present is about 5 times the mass of our sun, so most black holes have much greater mass than our Moon.

[edit] Techniques for finding black holes

[edit] Accretion disks and gas jets

Formation of extragalactic jets from a black hole's accretion disk

Most accretion disks and gas jets are not clear proof that a stellar-mass black hole is present, because other massive, ultra-dense objects such as neutron stars and white dwarfs cause accretion disks and gas jets to form and to behave in the same ways as those round black holes. But they can often help by telling astronomers where it might be worth looking for a black hole.

On the other hand, extremely large accretion disks and gas jets may be good evidence for the presence of supermassive black holes, because as far as we know any mass large enough to power these phenomena must be a black hole.

[edit] Strong radiation emissions

Steady X-ray and gamma ray emissions also do not prove that a black hole is present but can tell astronomers where it might be worth looking for one - and they have the advantage that they pass fairly easily through nebulae and gas clouds.

But strong, irregular emissions of X-rays, gamma rays and other electromagnetic radiation can help to prove that a massive, ultra-dense object is not a black hole, so that "black hole hunters" can move on to some other object. Neutron stars and other very dense stars have surfaces, and matter colliding with the surface at a high percentage of the speed of light will produce intense flares of radiation at irregular intervals. Black holes have no material surface, so the absence of irregular flares round a massive, ultra-dense object suggests that there is a good chance of finding a black hole there.

Intense but one-time gamma ray bursts (GRBs) may signal the birth of "new" black holes, because astrophysicists think that GRBs are caused either by the gravitational collapse of giant stars^[8] or by collisions between neutron stars,^[9] and both types of event involve sufficient mass and pressure to produce black holes. But it appears that a collision between a neutron star and a black hole can also cause a GRB,^[10] so a GRB is not proof that a "new" black hole has been formed. All known GRBs come from outside our own galaxy, and most come from billions of light years away^[11] so the black holes associated with them are actually billions of years old.

Some astrophysicists believe that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.^[12]

Quasars are thought to be caused by the accretion disks of supermassive black holes, since we know of nothing else which is powerful enough to produce such strong emissions. While X-rays and gamma rays have much higher frequencies and shorter wavelengths than visible light, quasars radiate mainly radio waves, which have lower frequencies and longer wavelengths than visible light.

[edit] Gravitational lensing

Gravitational lensing distorts the image around a black hole in front of the Large Magellanic Cloud (artistic interpretation)

Gravitational lensing is another phenomenon which can have other causes besides the presence of a black hole, because any very strong gravitational field bends light rays. The most spectacular examples produce multiple images of very distant objects by bending towards our telescopes light rays which would otherwise have gone in different directions. But these multiple-image effects are probably produced by distant galaxies.

[edit] Objects orbiting possible black holes

Some large celestial objects are almost certainly orbiting around black holes, and the principles behind this conclusion are surprisingly simple if we consider a circular orbit first (although all known astronomical orbits are elliptical):

• The radius of the central object round which the observed object is orbiting must be less than the radius of the orbit, otherwise the two objects would collide.
• The orbital period and the radius of the orbit make it easy to calculate the centrifugal force created by the orbiting object. Strictly speaking the centrifugal force also depends on the orbiting object's mass, but the next two steps show why we can get away with pretending this is a fixed number, e.g. 1.
• The gravitational attraction between the central object and the orbiting object must be exactly equal to the centrifugal force, otherwise the orbiting body would either spiral into the central object or drift away.
• The required gravitational attraction depends on the mass of the central object, the mass of the orbiting object and the radius of the orbit. But we can simplify the calculation of both the centrifugal force and the gravitational attraction by pretending that the mass of the orbiting object is the same fixed number, e.g. 1. This makes it very easy to calculate the mass of the central object.
• If the Schwarzschild radius for a body with the mass of the central object is greater than the maximum radius of the central object, the central object must be a black hole whose event horizon's radius is equal to the Schwarzschild radius.

Unfortunately in real astronomy there are some complications, but astronomers have been dealing with them for centuries (since the time of Kepler):

• Astronomical orbits are elliptical. This complicates the calculation of the centrifugal force, the gravitational attraction and the maximum radius of the central body. But Kepler could handle this without needing a computer.
• The orbital periods in this type of situation are several years, so several years' worth of observations are needed to determine the actual orbit accurately. The "possibly a black hole" indicators (accretion disks, gas jets, radiation emissions, etc.) help "black hole hunters" to decide which orbits are worth observing for such long periods.
• If there are other large bodies within a few light years, their gravity fields will perturb the orbit. Adjusting the calculations to filter out the effects of perturbation can be difficult, but astronomers are used to doing it.

[edit] Objects which are thought to be black holes

There is now a lot of indirect astronomical observational evidence for black holes in two mass ranges:

• stellar mass black holes with masses of a typical star (4–15 times the mass of our Sun), and
• supermassive black holes with masses ranging from on the order of 10⁵ to 10¹⁰ solar masses.

There is also some evidence for intermediate-mass black holes (IMBHs), those with masses of a few hundred to a few thousand times that of the Sun. These black holes may be responsible for the emission from ultraluminous X-ray sources (ULXs).

[edit] Supermassive black holes at the centers of galaxies

The jet originating from the center of M87 in this image comes from an active galactic nucleus that may contain a supermassive black hole. Credit: Hubble Space Telescope/NASA/ESA.

For decades, astronomers have used the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission^{[citation needed]}. However, theoretical and observational studies have shown that the active galactic nuclei in these galaxies may contain supermassive black holes^{[citation needed]}. The models of these active galactic nuclei consist of a central black hole that may be millions or billions times more massive than the Sun; a disk of gas and dust called an accretion disk; and two jets that are perpendicular to the accretion disk^{[citation needed]}.

Astronomers are confident that our own Milky Way galaxy has a supermassive black hole at its center, in a region called Sagittarius A*:

• A star called S2 follows an elliptical orbit with an period of 15.2 years and a pericenter (closest) distance of 17 light hours from the central object.
• The first estimates indicated that the central object contains 2.6M (2.6 million) solar masses and has a radius of less than 17 light hours. Only a black hole can contain such a vast mass in such a small volume.
• Further observations^[13] strengthened the case for a black hole by showing that the central object's mass is about 3.7M solar masses and its radius no more than 6.25 light-hours.

Evidence was reported in 2003 which suggested that the supermassive black hole at the center of the Milky Way is rotating at 50% of the maximum speed allowed by general relativity.^[14][15]

In 2004, astronomers found 31 probable supermassive black holes from searching obscured quasars. The lead scientist said that there are from two to five times as many supermassive black holes as previously predicted.^[16]

In June 2004 another team found a super-massive black hole, Q0906+6930, at the centre of a distant galaxy about 12.7 billion light years away. This observation indicated surprisingly rapid creation of super-massive black holes in the early universe.^[17]

[edit] Intermediate-mass black holes in globular clusters

In 2002, the Hubble Telescope produced observations indicating that globular clusters named M15 and G1 may contain intermediate-mass black holes. This interpretation is based on the sizes and periods of the orbits of the stars in the globular clusters. But the Hubble evidence is not conclusive, since a group of neutron stars could cause similar observations. Until recent discoveries, many astronomers thought that the complex gravitational interactions in globular clusters would eject newly-formed black holes.

In November 2004 a team of astronomers reported the discovery of the first well-confirmed intermediate-mass black hole in our Galaxy, orbiting three light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars, possibly the remnant of a massive star cluster that has been stripped down by the Galactic Centre.^[18][19] This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.

In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole, possibly of about 400 solar masses, in a globular cluster associated with a galaxy named NGC 4472, some 55 million light-years away.^[20]

[edit] Stellar-mass black holes in the Milky Way

Artist's impression of a binary system consisting of a black hole and a main sequence ("normal") star. The black hole is drawing matter from the main sequence star via an accretion disk around it, and some of this matter forms a gas jet.

Our Milky Way galaxy contains several probable stellar-mass black holes which are closer to us than the supermassive black hole in the Sagittarius A* region. These candidates are all members of X-ray binary systems in which the denser object draws matter from its partner via an accretion disk. The probable black holes in these pairs range from three to more than a dozen solar masses.^[21][22]

[edit] Micro black holes

The formation of micro black holes on Earth in particle accelerators has been tentatively reported,^[23] but not yet confirmed. So far there are no observed candidates for primordial black holes.

[edit] History of the black hole concept

The Newtonian conceptions of Michell and Laplace are often referred to as "dark stars" to distinguish them from the "black holes" of general relativity.

[edit] Newtonian theories (before Einstein)

The concept of a body so massive that even light could not escape was put forward by the geologist John Michell in a 1784 paper sent to Henry Cavendish and published by the Royal Society.^[24]

Michell's analysis is based on the concept of escape velocity, which can be deduced from Newton's Law of Gravitation. But Newton's Law of Gravitation assumes a pair of masses, not a single mass. So any analysis based on escape velocity assumes that photons have a non-zero rest mass (vis inertiae in the quote from Michell), but we now know that this is not true. The concept of escape velocity also allows an object to rise for an indefinite distance before falling back, and therefore does not predict event horizons round black holes.

In 1796, the mathematician Pierre-Simon Laplace promoted the same idea in the first and second editions of his book Exposition du système du Monde (it was removed from later editions).

The idea of black holes was largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity.

Note: before quantum mechanics was developed, physicists had been perplexed since about 1600 by the problem of wave-particle duality - some thought of light as a stream of particles, others thought of it as a series of waves, and the two different views went in and out of fashion alternately.

[edit] Theories based on Einstein's general relativity

In 1915, Albert Einstein developed the theory of gravity called general relativity, having earlier shown that gravity does influence light (although light has zero rest mass, its path follows any curvature of space-time, and gravity is curvature of space-time). A few months later, Karl Schwarzschild gave the solution for the gravitational field of a point mass and a spherical mass,^[25][26] showing that a black hole could theoretically exist. The Schwarzschild radius is now known to be the radius of the event horizon of a non-rotating black hole, but this was not well understood at that time, for example Schwarzschild himself thought it was not physical. Johannes Droste, a student of Lorentz, independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties.

In 1930, the astrophysicist Subrahmanyan Chandrasekhar argued that special relativity demonstrated that a non-radiating body above 1.44 solar masses (the Chandrasekhar limit), would collapse since there nothing known at that time could stop it from doing so. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Both were partly right: a white dwarf more massive than the Chandrasekhar limit will collapse into a neutron star; but a neutron star above about three solar masses (the Tolman-Oppenheimer-Volkoff limit) will itself collapse into a black hole for the reasons presented by Chandrasekhar.

In 1939, Robert Oppenheimer and H. Snyder predicted that massive stars could undergo a dramatic gravitational collapse, so theoretically black holes could, in principle, be formed in nature. Such objects for a while were called "frozen stars" since the collapse would be observed to rapidly slow down and become heavily redshifted near the Schwarzschild radius. The mathematics showed that an outside observer would see the surface of the star frozen in time at the instant where it crosses that radius.

These hypothetical objects were not the topic of much interest until the late 1960s. Most physicists believed that they were a peculiar feature of the highly symmetric solution found by Schwarzschild, and that objects collapsing in nature would not form black holes.

In 1967 astronomers discovered pulsars, and within a few years could show that the known pulsars were rapidly rotating neutron stars. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense object that might be formed by gravitational collapse.

In December 1967 the theoretical physicist John Wheeler coined the expression "black hole" in his public lecture Our Universe: the Known and Unknown, and this mysterious, slightly menacing phrase attracted more attention than the static-sounding "frozen star".

In 1970, Stephen Hawking and Roger Penrose proved that black holes are a feature of all solutions to Einstein's equations of gravity, not just of Schwarzschild's, and therefore black holes cannot be avoided in some collapsing objects.^[27]

[edit] Black holes and Earth

Black holes are sometimes listed among the most serious potential threats to Earth and humanity,^[28][29] on the grounds that:

• A naturally-produced black hole could pass through our Solar System.
• A large particle accelerator might produce a micro black hole, and if this escaped it could gradually eat the whole of the Earth.

[edit] Black hole wandering through our solar system

Stellar-mass black holes travel through the Milky Way just like stars. Consequently, they may collide with the Solar System or another planetary system in the galaxy, although the possibilities of this happening are very small. Significant gravitational interactions between the Sun and any other star in the Milky Way (including a black hole) are expected to occur approximately once every 10¹⁹ years.^[30] For comparison, the Sun has an age of only 5 × 10⁹ years, and it is only expected to burn hydrogen for fuel for another 5 × 10⁹ years^{[citation needed]}. Hence, the Sun will probably die out well before a black hole ever passes through the Solar System.

[edit] Micro black hole escaping from particle accelerator

There is a theoretical possibility that a micro black hole might be created inside a particle accelerator.^[31] Formation of black holes under these conditions (below the Planck energy) requires non-standard assumptions, such as large extra dimensions.

However, many particle collisions that naturally occur as the cosmic rays hit the edge of our atmosphere are often far more energetic than any collisions created by man. If micro black holes can be created by current or next-generation particle accelerators, they have probably been created by cosmic rays every day throughout most of Earth's history, i.e. for billions of years, evidently without earth-destroying effects.

Even if, say, two protons at the Large Hadron Collider could merge to create a micro black hole, this black hole would be extremely unstable, and it would vaporize due to Hawking radiation before it had a chance to propagate. For a 14 TeV black hole (the center-of-mass energy at the Large Hadron Collider), direct computation of its lifetime by the Hawking radiation formula indicates that it would evaporate in 10^-100 seconds.

CERN conducted a study assessing the risk of producing dangerous objects such as black holes at the Large Hadron Collider, and concluded that there is "no basis for any conceivable threat."^[32]

[edit] Alternative models

Several alternative models, which behave like a black hole but avoid the singularity, have been proposed. However, most researchers judge these concepts artificial, as they are more complicated but do not give near term observable differences from black holes (see Occam's razor). The most prominent alternative theory is the Gravastar.

In March 2005, physicist George Chapline at the Lawrence Livermore National Laboratory in California proposed that black holes do not exist, and that objects currently thought to be black holes are actually dark-energy stars. He draws this conclusion from some quantum mechanical analyses. Although his proposal currently has little support in the physics community, it was widely reported by the media.^[33][34]

Among the alternate models are magnetospheric eternally collapsing objects, clusters of elementary particles^[35] (e.g., boson stars^[36]), fermion balls,^[37] self-gravitating, degenerate heavy neutrinos^[38] and even clusters of very low mass (~0.04 solar mass) black holes.^[35]

[edit] More advanced topics

[edit] Entropy and Hawking radiation

In 1971, Stephen Hawking showed that the total area of the event horizons of any collection of classical black holes can never decrease. This sounded remarkably similar to the Second Law of Thermodynamics, with area playing the role of entropy. Classically, one could violate the second law of thermodynamics by material entering a black hole disappearing from our universe and resulting in a decrease of the total entropy of the universe. Therefore, Jacob Bekenstein proposed that a black hole should have an entropy and that it should be proportional to its horizon area. Since black holes do not classically emit radiation, the thermodynamic viewpoint was simply an analogy. However, in 1974, Hawking applied quantum field theory to the curved spacetime around the event horizon and discovered that black holes can emit Hawking radiation, a form of thermal radiation. Using the first law of black hole mechanics, it follows that the entropy of a black hole is one quarter of the area of the horizon. This is a universal result and can be extended to apply to cosmological horizons such as in de Sitter space. It was later suggested that black holes are maximum-entropy objects, meaning that the maximum entropy of a region of space is the entropy of the largest black hole that can fit into it. This led to the holographic principle.

The Hawking radiation reflects a characteristic temperature of the black hole, which can be calculated from its entropy. This temperature in fact falls the more massive a black hole becomes: the more energy a black hole absorbs, the colder it gets. A black hole with roughly the mass of the planet Mercury would have a temperature in equilibrium with the cosmic microwave background radiation (about 2.73 K). More massive than this, a black hole will be colder than the background radiation, and it will gain energy from the background faster than it gives energy up through Hawking radiation, becoming even colder still. However, for a less massive black hole the effect implies that the mass of the black hole will slowly evaporate with time, with the black hole becoming hotter and hotter as it does so. Although these effects are negligible for black holes massive enough to have been formed astronomically, they would rapidly become significant for hypothetical smaller black holes, where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and eventually vanish in a burst of radiation.

If ultra-high-energy collisions of particles in a particle accelerator can create microscopic black holes, it is expected that all types of particles will be emitted by black hole evaporation, providing key evidence for any grand unified theory. Above are the high energy particles produced in a gold ion collision on the RHIC.

Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In statistical mechanics, entropy is understood as counting the number of microscopic configurations of a system which have the same macroscopic qualities(such as mass, charge, pressure, etc.). But without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes. Some promise has been shown by string theory, however. There one posits that the microscopic degrees of freedom of the black hole are D-branes. By counting the states of D-branes with given charges and energy, the entropy for certain supersymmetric black holes has been reproduced. Extending the region of validity of these calculations is an ongoing area of research.

[edit] Black hole unitarity

An open question in fundamental physics is the so-called information loss paradox, or black hole unitarity paradox. Classically, the laws of physics are the same run forward or in reverse. That is, if the position and velocity of every particle in the universe were measured, we could (disregarding chaos) work backwards to discover the history of the universe arbitrarily far in the past. In quantum mechanics, this corresponds to a vital property called unitarity which has to do with the conservation of probability.

Black holes, however, might violate this rule. The position under classical general relativity is subtle but straightforward: because of the classical no hair theorem, we can never determine what went into the black hole. However, as seen from the outside, information is never actually destroyed, as matter falling into the black hole appears from the outside to become more and more red-shifted as it approaches (but never ultimately appears to reach) the event horizon.

Ideas of quantum gravity, on the other hand, suggest that there can only be a limited finite entropy (ie a maximum finite amount of information) associated with the space near the horizon; but the change in the entropy of the horizon plus the entropy of the Hawking radiation is always sufficient to take up all of the entropy of matter and energy falling into the black hole.

Many physicists are concerned however that this is still not sufficiently well understood. In particular, at a quantum level, is the quantum state of the Hawking radiation uniquely determined by the history of what has fallen into the black hole; and is the history of what has fallen into the black hole uniquely determined by the quantum state of the black hole and the radiation? This is what determinism, and unitarity, would require.

For a long time Stephen Hawking had opposed such ideas, holding to his original 1975 position that the Hawking radiation is entirely thermal and therefore entirely random, representing new nondeterministically created information. However, on 21 July 2004 he presented a new argument, reversing his previous position.^[39] On this new calculation, the entropy associated with the black hole itself would still be inaccessible to external observers; and in the absence of this information, it is impossible to relate in a 1:1 way the information in the Hawking radiation (embodied in its detailed internal correlations) to the initial state of the system. However, if the black hole evaporates completely, then such an identification can be made, and unitarity is preserved. It is not clear how far even the specialist scientific community is yet persuaded by the mathematical machinery Hawking has used (indeed many regard all work on quantum gravity so far as highly speculative); but Hawking himself found it sufficiently convincing to pay out on a bet he had made in 1997 with Caltech physicist John Preskill, to considerable media interest.

[edit] Mathematical theory

Further information: Schwarzschild metric  and Deriving the Schwarzschild solution

Black holes are predictions of Albert Einstein's theory of general relativity. There are many known solutions to the Einstein field equations which describe black holes, and they are also thought to be an inevitable part of the evolution of any star of a certain size. In particular, they occur in the Schwarzschild metric, one of the earliest and simplest solutions to Einstein's equations, found by Karl Schwarzschild in 1915. This solution describes the curvature of spacetime in the vicinity of a static and spherically symmetric object, where the metric is,

,

where is a standard element of solid angle.

According to general relativity, a gravitating object will collapse into a black hole if its radius is smaller than a characteristic distance, known as the Schwarzschild radius. (Indeed, Buchdahl's theorem in general relativity shows that in the case of a perfect fluid model of a compact object, the true lower limit is somewhat larger than the Schwarzschild radius.) Below this radius, spacetime is so strongly curved that any light ray emitted in this region, regardless of the direction in which it is emitted, will travel towards the centre of the system. Because relativity forbids anything from traveling faster than light, anything below the Schwarzschild radius – including the constituent particles of the gravitating object – will collapse into the centre. A gravitational singularity, a region of theoretically infinite density, forms at this point. Because not even light can escape from within the Schwarzschild radius, a classical black hole would truly appear black.

The Schwarzschild radius is given by

where G is the gravitational constant, m is the mass of the object, and c is the speed of light. For an object with the mass of the Earth, the Schwarzschild radius is a mere 9 millimeters — about the size of a marble.

The mean density inside the Schwarzschild radius decreases as the mass of the black hole increases, so while an earth-mass black hole would have a density of 2 × 10³⁰ kg/m³, a supermassive black hole of 10⁹ solar masses has a density of around 20 kg/m³, less than water! The mean density is given by

Since the Earth has a mean radius of 6371 km, its volume would have to be reduced 4 × 10²⁶ times to collapse into a black hole. For an object with the mass of the Sun, the Schwarzschild radius is approximately 3 km, much smaller than the Sun's current radius of about 696,000 km. It is also significantly smaller than the radius to which the Sun will ultimately shrink after exhausting its nuclear fuel, which is several thousand kilometers. More massive stars can collapse into black holes at the end of their lifetimes.

The formula also implies that any object with a given mean density is a black hole if its radius is large enough. The same formula applies for white holes as well. For example, if the observable universe has a mean density equal to the critical density, then it is a white hole, since its singularity is in the past and not in the future as should be for a black hole.

More general black holes are also predicted by other solutions to Einstein's equations, such as the Kerr metric for a rotating black hole, which possesses a ring singularity. Then we have the Reissner-Nordström metric for charged black holes. Last the Kerr-Newman metric is for the case of a charged and rotating black hole.

There is also the Black Hole Entropy formula:

Where A is the area of the event horizon of the black hole, is Dirac's constant (the "reduced Planck constant"), k is the Boltzmann constant, G is the gravitational constant, c is the speed of light and S is the entropy.

A convenient length scale to measure black hole processes is the "gravitational radius", which is equal to

When expressed in terms of this length scale, many phenomena appear at integer radii. For example, the radius of a Schwarzschild black hole is two gravitational radii and the radius of a maximally rotating Kerr black hole is one gravitational radius. The location of the light circularization radius around a Schwarzschild black hole (where light may orbit the hole in an unstable circular orbit) is 3r_G. The location of the marginally stable orbit, thought to be close to the inner edge of an accretion disk, is at 6r_G for a Schwarzschild black hole.

[edit] Notes

[edit] References

[edit] Popular reading

• Hawking, Stephen (1998). A Brief History of Time. Bantam Books, Inc. ISBN 0-553-38016-8. 
• Pickover, Clifford (1998). Black Holes: A Traveler's Guide. Wiley, John & Sons, Inc. ISBN 0-471-19704-1. 
• Ferguson, Kitty (1991). Black Holes in Space-Time. Watts Franklin. ISBN 0-531-12524-6. 
• Thorne, Kip S. (1994). Black Holes and Time Warps. Norton, W. W. & Company, Inc. ISBN 0-393-31276-3. 

[edit] University textbooks and monographs

• Wald, Robert M. (1992). Space, Time, and Gravity: The Theory of the Big Bang and Black Holes. University of Chicago Press. ISBN 0-226-87029-4. 
• Chandrasekhar, Subrahmanyan (1999). Mathematical Theory of Black Holes. Oxford University Press. ISBN 0-19-850370-9. 
• Thorne, Kip S.; Misner, Charles; Wheeler, John (1973). Gravitation. W. H. Freeman and Company. ISBN 0-7167-0344-0. 
• Carter, B. (1973). Black hole equilibrium states, in Black Holes, eds. DeWitt B. S. and DeWitt C.
• Frolov, V. P. and Novikov, I. D. (1998), Black hole physics.
• Hawking, S. W. and Ellis, G. F. R. (1973), The large-scale structure of space-time, Cambridge University Press.

[edit] Research papers

• Hawking, S. W. (July 2005), Information Loss in Black Holes, arxiv:hep-th/0507171. Stephen Hawking's purported solution to the black hole unitarity paradox, first reported at a conference in July 2004.
• Ghez, A.M. et al. Stellar orbits around the Galactic Center black hole, Astrophysics J. 620 (2005). arXiv:astro-ph/0306130 More accurate mass and position for the black hole at the centre of the Milky Way.
• Hughes, S. A. Trust but verify: the case for astrophysical black holes, arXiv:hep-ph/0511217. Lecture notes from 2005 SLAC Summer Institute.

[edit] External links

• Anatomy of a Black Hole
• Black Holes: Gravity's Relentless Pull - Award-winning interactive multimedia Web site about the physics and astronomy of black holes from the Space Telescope Science Institute
• FAQ on black holes
• Schwarzschild Geometry on Andrew Hamilton’s website
• Black Hole in Knowledge storage
• Tufts University: Student Project (Great Kid's Section)
• Movie of Black Hole Candidate from Max Planck Institute
• UT Brownsville Group Simulates Spinning Black-Hole Binaries 13 April 2006
• Black Hole Research News on ScienceDaily
• Scientific American Magazine (July 2003 Issue) The Galactic Odd Couple - giant black holes and stellar baby booms
• Scientific American Magazine (May 2005 Issue) Quantum Black Holes
• SPACE.com All About Black Holes - News, Features and Interesting Original Videos
• Black holes explained - Information about Black Holes at larger-than-life.org
• Black Holes Intro - Introduction to Black Holes
• HowStuffWorks: How Black Holes Work - Easy to consume guide to Black Holes
• Ted Bunn's Black Holes FAQ explains in simple language some other consequences of the way in which black holes bend space-time.