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# Black hole

A black hole is a concentration of mass with a gravitational field so strong that the escape velocity from nearby points exceeds the speed of light. This implies that nothing, not even light, can escape its gravity, hence the word "black." The term "black hole" is widespread, even though the theory does not refer to any hole in the usual sense, but rather a region of space from which nothing can return.

Black holes are predicted by general relativity. According to classical general relativity, no matter or information can flow from the interior of a black hole to an outside observer (e.g., one cannot bring out any of its mass, or receive a reflection back by shining a light source such as a flashlight, or retrieve any information about the material that has entered the black hole), although quantum mechanics may allow deviations from this strict rule. The existence of black holes in the universe is well supported both theoretically and by astronomical observation.

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## History

The concept of a body so massive that not even light could escape from it was put forward by the English geologist John Michell in a 1783 paper sent to the Royal Society. At that time, the Newtonian theory of gravity and the concept of escape velocity were well known. Michell computed that a body 500 times the radius of the Sun and of the same density would have at its surface an escape velocity equal to the speed of light, and therefore would be invisible. In his words:

If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae (inertial mass), with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity.

Although he thought it unlikely, Michell considered the possibility that many such objects that cannot be seen might be present in the cosmos.

In 1796, the French mathematician Pierre-Simon Laplace promoted the same idea in the first and second edition of his book Exposition du Systeme du Monde . It disappeared in later editions. The whole idea gained little attention in the 19th century, since light was thought to be a massless wave, not influenced by gravity.

In 1915 Einstein developed the theory of gravity called General Relativity. Earlier he had shown that gravity does influence light. A few months later Karl Schwarzschild gave the solution for the gravitational field of a point mass, showing that something we now call a black hole could theoretically exist. The Schwarzschild radius is now known to be the radius of a non-rotating black hole, but was not well understood at that time. Schwarzschild himself thought it not to be physical.

In the 1920s, Subrahmanyan Chandrasekhar argued that special relativity demonstrated that a non-radiating body above a certain mass, now known as the Chandrasekhar limit, would collapse since there would be nothing that could stop the collapse. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse.

In 1939 Robert Oppenheimer and H. Snyder predicted that massive stars could undergo a dramatic gravitational collapse. 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 reddened near the Schwarzschild radius. However, these hypothetical objects were not the topic of much theoretical interest until the late 1960s.

Interest in collapsed objects was rekindled in 1967 with the discovery of pulsars. Shortly thereafter, the use of the expression "black hole" was coined by theoretical physicist John Wheeler [1] http://www.truephysics.com/timeline/timeline1961_1980.html . Prior to that time, the term black star was used occasionally. The term appears in an early episode of Star Trek, and was still used occasionally after 1967. This is because some people found the term "black hole" obscene when translated into French or Russian, for example.

## Qualitative physics

Black holes as they are most widely understood require general relativity's concept of a curved spacetime, since their most striking properties rely on a distortion of the geometry of the space surrounding them.

### The event horizon

The "surface" of a black hole is the so-called event horizon, an imaginary spheroidal surface surrounding all the hole's mass. At the event horizon, the escape velocity is equal to the speed of light. Thus, anything inside the event horizon, including a photon, is prevented from reaching the event horizon by the extremely strong gravitational field. Particles from outside this region can fall in, cross the event horizon, and will never be able to leave.

Since no particles can leave the interior, there is no way of sending information from inside the event horizon to an observer outside it. Black holes have no observable external characteristics that can be used to determine what they are like inside. According to classical general relativity, black holes can be entirely characterized according to three parameters: mass, angular momentum and electric charge. This principle is summarized by the saying "black holes have no hair."

Objects in a gravitational field experience a slowing down of time, called time dilation. This phenomenon has been verified experimentally in the Scout rocket experiment of 1976 [2] http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html . Near a black hole, the time dilation increases to a large degree. From the point of view of an external observer, it appears to take an infinite amount of time for an object to approach the event horizon, at which point the light coming from it is infinitely red-shifted. To the distant observer, it appears that the object, falling more and more slowly, approaches but never reaches the event horizon (i.e., takes an infinite amount of time to reach it). From the point of view of the infalling object itself, however, it will take a finite time to cross the event horizon and reach the singularity.

### The singularity

At the center of the event horizon is a singularity, a place where general relativity predicts that spacetime becomes infinitely curved (i.e., where gravity becomes infinitely strong). Spacetime inside the event horizon is peculiar in that the singularity is literally the only possible future, so all particles within the event horizon must move inexorably towards it (Penrose and Hawking [3] http://www.maths.soton.ac.uk/relativity/GRExplorer/singularities/singtheorems.ht
m
). This means that there is a conceptual inaccuracy in the nonrelativistic concept of a black hole as originally proposed by John Michell in 1783. In Michell's theory, the escape velocity equals the speed of light, but it would still, for example, be theoretically possible to hoist an object out of a black hole using a rope. General relativity eliminates such loopholes, because once an object is inside the event horizon, its time-line contains an end-point to time itself, and no possible world-lines cross the event horizon.

It is expected that future refinements or replacements of general relativity (in particular quantum gravity) will change what is thought about the nature of black hole interiors. Most theorists interpret the mathematical singularity of the equations as indicating that the current theory is not complete, and that new phenomena must come into play as one approaches the singularity.

### Falling in

Consider a hapless astronaut falling feet first radially towards the center of a simple Schwarzschild-type (non-rotating) black hole. The closer he gets to the event horizon, the longer the photons he emits take to escape from the black hole's gravitational field. A distant observer will see the astronaut's descent slowing as he approaches the event horizon, which he never appears to reach.

However, in his own frame of reference, the astronaut will cross the event horizon and reach the singularity, all in a finite amount of time. Once he has crossed the event horizon he can no longer be observed from the outside universe. As he falls, he will notice his feet, then his knees, becoming increasingly red-shifted until they appear invisible. As he nears the singularity, the gradient of the gravitational field from head to foot will become considerable, and he will feel stretched, and finally torn. This process is known as spaghettification. This gradient becomes large enough, close to the singularity, to tear atoms apart. The point at which these tidal forces become fatal depends on the size of the black hole. For a very large black hole such as those found at the center of galaxies, this point will lie well inside the event horizon, so the astronaut may cross the event horizon painlessly. Conversely, for a small black hole, those tidal effects may become fatal long before the astronaut reaches the event horizon.

### Rotating black holes

According to theory, the event horizon of a black hole that is not spinning is spherical, and its singularity is (informally speaking) a single point. If the black hole carries angular momentum (inherited from a star that is spinning at the time of its collapse), it begins to drag space-time surrounding the event horizon in an effect known as frame-dragging. This spinning area surrounding the event horizon is called the ergosphere and has an ellipsoidal shape. Since the ergosphere is located outside the event horizon, objects can exist within the ergosphere without inevitably falling into the hole. However, because space-time itself is moving in the ergosphere, it is impossible for objects to remain in a fixed position. Objects grazing the ergosphere could in some circumstances be catapulted outwards at great speed, extracting energy (and angular momentum) from the hole, hence the name ergosphere ("sphere of work") because it is capable of doing work.

### Entropy and Hawking radiation

In 1971, Stephen Hawking showed that the total event horizon area 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. Therefore, Jacob Bekenstein proposed that the entropy of a black hole really is proportional to its horizon area. In 1975, Hawking applied quantum field theory to a semi-classical curved spacetime and discovered that black holes can emit thermal radiation, known as Hawking radiation. This allowed him to calculate the entropy, which indeed was proportional to the area, validating Bekenstein's hypothesis. It was later discovered 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 proposal of the holographic principle.

Hawking radiation originates just outside the event horizon and (semi-classically) does not carry information from its interior. However, this means that black holes are not completely black. Moreover, the effect implies that the mass of a black hole slowly evaporates with time. Although these effects are negligible for astronomical-sized objects, they are significant for hypothetical very small black holes where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and will therefore eventually vanish in a burst of radiation. Hence, every black hole that cannot consume new mass has a finite life that is directly related to its mass.

On 21 July 2004 Stephen Hawking presented a new argument that black holes do eventually emit information about what they swallow, reversing his previous position on information loss. He proposed that quantum perturbations of the event horizon could allow information to escape from a black hole, where it can influence subsequent Hawking radiation [4] http://www.nature.com/news/2004/040712/full/040712-12.html . The theory is still undergoing review, and if it is accepted it is likely to resolve the black hole information paradox. In the meantime, the announcement has attracted a lot of attention in the media.

## Reality of black holes

### Do black holes exist?

General relativity (as well as most other metric theories of gravity) not only says that black holes can exist, but in fact predicts that they will be formed in nature whenever a sufficient amount of mass gets packed in a given region of space, through a process called gravitational collapse. As the mass inside that region increases, its gravity becomes stronger — or, in the language of relativity, the space around it becomes increasingly deformed. When the escape velocity at a certain distance from the center reaches the speed of light, an event horizon is formed within which matter must inevitably collapse onto a single point, forming a singularity.

A quantitative analysis of this idea led to the prediction that a star remaining about three times the mass of the Sun at the end of its evolution (usually as a neutron star), will almost inevitably shrink to the critical size needed to undergo a gravitational collapse. Once it starts, the collapse cannot be stopped by any physical force, and a black hole is created.

Stellar collapse will generate black holes containing at least three solar masses. Black holes smaller than this limit can only be created if their matter is subjected to sufficient pressure from some source other than self-gravitation. The enormous pressures needed for this are thought to have existed in the very early stages of the universe, possibly creating primordial black holes which could have masses smaller than that of the Sun.

Supermassive black holes containing millions to billions of solar masses could also form wherever a large number of stars are packed in a relatively small region of space, or by large amounts of mass falling into a "seed" black hole, or by repeated fusion of smaller black holes. The necessary conditions are believed to exist in the centers of some (if not most) galaxies, including our own Milky Way.

### Can they be discovered?

Theory says that we cannot detect black holes by light that is emitted or reflected by the matter inside them. However, those objects can be inductively detected from observation of phenomena near them, such as gravitational lensing and stars that appear to be in orbit around space where there is no visible matter.

The most conspicuous effects are believed to come from matter falling into a black hole, which (like water flowing into a drain) is predicted to collect into an extremely hot and fast-spinning accretion disk around the object before being swallowed by it. Friction between adjacent zones of the disk causes it to become extremely hot and emit large amounts of X-rays. This heating is extremely efficient and can convert about 50% of the mass energy of an object into radiation, as opposed to nuclear fusion which can only convert a few percent of the mass to energy. Other predicted effects are narrow jets of particles at relativistic speeds squirting off along the disk's axis.

However, accretion disks, jets, and orbiting objects are found not only around black holes, but also around other objects such as neutron stars; and the dynamics of bodies near these non-black hole attractors is largely similar to the dynamics of bodies around black holes, and is current a very complex and active field of research involving magnetic fields and plasma physics. Hence, for the most part, observations of accretion disks and orbital motions merely indicate that there is a compact object of a certain mass, and says very little about the nature of that object. The identification of an object as a black hole requires the further assumption that no other object (or bound system of objects) could be so massive and compact. Most astrophysicists accept that this is the case, since according to general relativity, any concentration of matter of sufficient density must necessarily collapse into a black hole.

One important observable difference between black holes and other compact massive objects is that any infalling matter will eventually collide with the latter, at relativistic speeds, leading to irregular intense flares of X-rays and other hard radiation. Thus the lack of such flare-ups around a compact concentration of mass is taken as evidence that the object is a black hole, with no surface onto which matter can be suddenly dumped.

### Have we found them?

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

(This evidence comes not from seeing the black holes directly, but by observing the behavior of stars and other material near them).

Additionally, there is some evidence for intermediate-mass black holes (IMBHs), those with masses of a few thousand times that of the Sun. These black holes may be responsible for the formation of supermassive black holes.

Candidates to stellar-mass black holes were identified mainly by the presence of accretion disks of the right size and speed, without the irregular flare-ups that are expected from disks around other compact objects. Stellar-mass black holes may be involved in gamma ray bursts (GRBs), although observations of GRBs in association with supernovae or other objects that are not black holes [5] http://liftoff.msfc.nasa.gov/academy/universe/plasma_univ.html [6] http://www.wkap.nl/prod/b/0-7923-3784-0 have reduced the possibility of a link.

Candidates for more massive black holes were first provided by the active galactic nuclei and quasars, discovered by radioastronomers in the 1960s. The efficient conversion of mass into energy by friction in the accretion disk of a black hole seems to be the only explanation for the copious amounts of energy generated by such objects. Indeed the introduction of this theory in the 1970s removed a major objection to the belief that quasars were distant galaxies — namely, that no physical mechanism could generate that much energy.

From observations in the 1980s of motions of stars around the galactic center, it is now believed that such supermassive black holes exist in the center of most galaxies, including our own Milky Way. Sagittarius A* is now agreed to be the most plausible candidate for the location of a supermassive black hole at the center of the Milky Way galaxy.

The current picture is that all galaxies may have a supermassive black hole in their center, and that this black hole swallows gas and dust in the middle of the galaxies generating huge amounts of radiation — until all the nearby mass has been swallowed and the process shuts off. This picture also nicely explains why there are no nearby quasars. Though the details are still not clear, it seems that the growth of the black hole is intimately related to the growth of the spheroidal component — an elliptical galaxy, or the bulge of a spiral galaxy — in which it lives. Interestingly, there is no evidence for massive black holes in the center of globular clusters, suggesting that these are fundamentally different from galaxies.

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

## Mathematical physics

Black holes are predictions of Albert Einstein's theory of general relativity. 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

$ds^2 = - \left( 1 - {2M \over r} \right) dt^2 + \left( 1 - {2M \over r} \right)^{-1} dr^2 + r^2 d\Omega^2$,

where relativistic units c = G = 1 are used and $d\Omega^2 = d\theta^2 + \cos^2\theta\; d\phi^2$ is a standard element of solid angle.

According to Schwarzschild's solution, a gravitating object will collapse into a black hole if its radius is smaller than a characteristic distance, known as 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 center of the system. Because relativity forbids anything from travelling faster than light, anything below the Schwarzschild radius – including the constituent particles of the gravitating object – will collapse into the center. 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 rs = 2M in relativistic units as above, or

$r_s = {2\,GM \over c^2}$

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

$\rho=\frac{3\,c^6}{32\pi M^2G^3}$

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 700,000 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.

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, and the Reissner-Nordstrøm metric for charged black holes.

## Recent discoveries

In 2004 a cluster of black holes was detected, broadening our understanding of the distribution of black holes throughout our universe. This has led scientists' inferences of how many black holes are in our universe to be significantly revised. It is believed due to these finds in 2004 that there are close to five fold the number of black holes than were previously predicted.

In July 2004 astronomers found a giant black hole, Q0906+6930, at the center of a distant galaxy in the Ursa Major constellation. The size and presumed age of the black hole has implications that may determine the age of the universe [7] http://www.space.com/scienceastronomy/heavy_blazar_040628.html .

In November 2004 a team of astronomers reported the discovery of the first intermediate-mass black hole in our Galaxy, orbiting three light-years from Sagittarius A*. This medium 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.(Nature News) http://www.nature.com/news/2004/041108//full/041108-2.html#B2 (original article) http://edpsciences.nao.ac.jp/articles/aa/abs/2004/31/aa0147-03/aa0147-03.html This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.

## Related topics

• FAQ on black holes http://antwrp.gsfc.nasa.gov/htmltest/gifcity/bh_pub_faq.html
• Schwarzschild Geometry http://casa.colorado.edu/~ajsh/schwp.html
• An extensive look at the formation & life of a Black Hole http://www.armageddononline.org/blackhole.php
• Tufts University: Student Project (Great Kid's Section) http://hepguru.com/blackholes/
• Hong Kong University:Some information about Space http://www.lcsd.gov.hk/CE/Museum/Space/EducationResource/Universe/framed_e/index
.html
• Jilian’s Guide to Black Holes http://www.dragonweave.com/gothos/html/black_holes/index.html
• Supermassive Black Holes http://csep10.phys.utk.edu/astr162/lect/active/smblack.html
• Universe Today http://www.universetoday.com/am/publish/blackholes.html Black hole news stories