User:TimothyRias/temp2
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A black hole is an object predicted by general relativity,[1] with a gravitational field so powerful that even electromagnetic radiation (such as light) cannot escape its pull.[2] A black hole is defined to be a region of space-time where escape to the outside universe is impossible. The outer boundary of this region is called the event horizon. Nothing can move from inside the event horizon to the outside, even briefly, due to the extreme gravitational field existing within the region. For the same reason, observers outside the event horizon cannot see any events which may be happening within the event horizon; thus any energy being radiated or events happening within the region are forever unable to be seen or detected from outside. Within the black hole is a singularity, an anomalous place where matter is compressed to the degree that the known laws of physics no longer apply to it.
Theoretically, a black hole can be of any size. Astrophysicists expect to find black holes with masses ranging between roughly the mass of the Sun ("stellar-mass" black holes) to many millions of times the mass of the Sun (supermassive black holes).
The existence of black holes in the universe is well supported by astronomical observation, particularly from studying X-ray emission from X-ray binaries and active galactic nuclei. It has also been hypothesized that black holes radiate an undetectably small amount of energy due to quantum mechanical effects. This is called Hawking radiation.
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[edit] Simple overview
Most planets and other celestial bodies are stable because the Pauli force between electrons prevents atoms from collapsing into each other, while gravity, electromagnetism, and the strong force pull them together. These opposing forces create a balance which allows material bodies to retain their shape and structure. In extreme circumstances, however, if there is enough matter in a small enough space, gravity ends up winning, and the matter collapses: electrons cannot stay distant from the atomic nucleus, and incredibly dense matter forms (sometimes called neutronium).
If an even greater amount of mass is contained within the same space, even the Pauli force between nucleons cannot resist gravity and the body collapses into itself forming a black hole. In a way that can be hard to imagine, nothing can stop this collapse if enough matter gets into a small enough space, and the matter collapses to a point of zero height, width, and depth, known as a singularity. The mass in a singularity is so dense it is no longer "matter" in any real sense, but some kind of anomaly in space. Anything that gets too close to this singularity will also collapse into it the same way, whether it is matter, energy or even light itself, which is the fastest thing in the universe. The failure of even light to escape its gravitation is how this phenomenon initially acquired the name black hole.
Because matter and energy that pass this "boundary" can never escape back again, observers outside this invisible "boundary" can neither see inside nor detect what might happen within the interior — it is forever hidden from view. The invisible 'dividing line' in space where matter or energy will be unavoidably drawn into the black hole is known as the event horizon, because, like the earth's horizon, nothing can be seen beyond it.
It was later found that energy can escape from black holes in an unexpected way, and that therefore black holes can evaporate. In space, virtual particles are continually coming into existence and vanishing on a microscopic scale that is so small they cannot easily be detected. This is a consequence of quantum physics and only works on a subatomic scale. Conceptually, these particles can be imagined to appear in pairs and vanish a tiny fraction of a second later again. For this reason they are not readily noticed. But close to the black hole's event horizon, the intense gravitational field separates the two particles even in the fractional second that they exist. One particle may be absorbed into the black hole, the other escapes. From an external perspective all that is seen is the second of these, giving the appearance of energy being radiated outward, escaping from its gravitational field beyond the event horizon. In this way, paradoxically, black holes can evaporate. This process is thought to be significant for the very smallest black holes, as a black hole of stellar mass or larger would absorb more energy from cosmic microwave background radiation than they lose this way. The radiation emitted is referred to as Hawking radiation.
Black holes generally come in two types: those with a mass up to ten times the mass of our Sun, and those with a mass that is millions or billions of times that of our sun. The latter are called supermassive black holes, and are thought to exist at the centers of galaxies.[3] Micro black holes are believed to be possible but very short-lived, capable of creation under extreme circumstances such as the Big Bang or perhaps by very high powered particle accelerators or ultra-high-energy cosmic rays.[4]
[edit] History
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.[5] At that time, the Newtonian theory of gravity and the concept of escape velocity were well known. Michell computed that a body with 500 times the radius of the Sun and of the same density would have, at its surface, an escape velocity exceeding that of 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. | ” |
Michell considered the possibility that many such objects that cannot be seen might be present in the cosmos.
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 gained little attention in the nineteenth century, since light was thought to be a massless wave, hence not influenced by gravity.
In 1915, Albert Einstein developed the theory of gravity called general relativity, having earlier shown that gravity does influence light. A few months later, Karl Schwarzschild gave the solution for the gravitational field of a point mass and a spherical mass,[6][7] 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. Schwarzschild himself thought it was not physical. A few months after Schwarzschild, a student of Lorentz, Johannes Droste, independently gave the same solution for the point mass 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, now known as the Chandrasekhar limit, would collapse since there was nothing known at that time that could stop it from doing so. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Both were correct, since a white dwarf more massive than the Chandrasekhar limit will collapse into a neutron star. However, a neutron star above about three solar masses (the Tolman-Oppenheimer-Volkoff limit) will itself become unstable against collapse due to similar physics.
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 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.
Interest in black holes was rekindled in 1967 when this girl Alex had a baby and she discovered that the baby went to the bathroom. because of theoretical and experimental progress. In 1970, Stephen Hawking and Roger Penrose proved that black holes are a generic feature in Einstein's theory of gravity, and cannot be avoided in some collapsing objects.[1] Interest was renewed in the astronomical community with the discovery of pulsars. Shortly thereafter, the expression "black hole" was coined by theoretical physicist John Wheeler,[8] being first used in his public lecture Our Universe: the Known and Unknown on 29 December 1967. The older Newtonian objects of Michell and Laplace are often referred to as "dark stars" to distinguish them from the "black holes" of general relativity.
[edit] Evidence
[edit] Formation and size
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 the given region of space increases, its gravity becomes stronger and (in the language of relativity) increasingly deforms the space around it, until ultimately nothing (not even light) can escape the gravity; at this point an event horizon is formed, and matter and energy must inevitably collapse to a density beyond the limits of known physics. For example, if the Sun was compressed to a radius of roughly three kilometers (about 1/232,000 its present radius or 1/1.2487×1016 of its initial volume), the resulting gravitational field would create an event horizon around it, and thus a black hole.
A quantitative analysis of this idea led to the prediction that a stellar remnant above about three to five times the mass of the Sun (the Tolman-Oppenheimer-Volkoff limit) would be unable to support itself as a neutron star via degeneracy pressure, and would inevitably collapse into a black hole. Stellar remnants with this mass are expected to be produced immediately at the end of the lives of stars that are more than 25 to 50 times the mass of the Sun, or by accretion of matter onto an existing neutron star.
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 are believed to exist in the center of most galaxies, including our own Milky Way. This type of black hole contains millions to billions of solar masses, and there are several models of how they might have been formed. The first is via gravitational collapse of a dense cluster of stars. A second is by large amounts of mass accreting onto a "seed" black hole of stellar mass. A third is by repeated fusion of smaller black holes. Effects of such supermassive black holes on spacetime may be observed in regions as the Virgo Cluster of galaxies, for example, the location of M87 (see image below) and its neighbors.
Intermediate-mass black holes have a mass between that of stellar and supermassive black holes, typically in the range of thousands of solar masses. Intermediate-mass black holes have been proposed as a possible power source for ultra-luminous X ray sources, and in 2004 detection was claimed of an intermediate-mass black hole orbiting the Sagittarius A* supermassive black hole candidate at the core of the Milky Way galaxy. This detection is disputed.
The lower limit on the mass of a black hole comes from the quantum arguments. According to the most commonly accepted physics, one should not expect to observe black holes lighter than the Planck mass, or approximately 10-5 g, and even those would only exist for minuscule periods of time before evaporating. If true, this limit would rule out the possibility of creating miniature black holes in the laboratory in the foreseeable future: even today, center-of-mass collision energies of the world's most advanced particle accelerators are still 14–15 orders of magnitude lower than the Planck mass.
However, certain models of unification of the four fundamental forces do allow the formation of micro black holes under laboratory conditions. These 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, though even a negative result improves constraints on compactification of extra dimensions from string theory or other models of physics.
[edit] Observation
In theory, no object within the event horizon of a black hole can ever escape, including light. However, black holes can be inductively detected from observation of phenomena near them, such as gravitational lensing, galactic jets, and stars that appear to be in orbit (typically with short orbital periods of only a few hours or days suggesting a massive partner) around a point in space where there is no visible matter.
The most conspicuous effects are believed to come from matter accreting onto a black hole, which is predicted to collect into an extremely hot and fast-spinning accretion disk. The internal viscosity of the disk causes it to become extremely hot, and emit large amounts of X-ray and ultraviolet radiation. This process is extremely efficient and can convert about 10% of the rest 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 observed effects are narrow jets of particles at relativistic speeds heading 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 white dwarfs; and the dynamics of bodies near these non-black hole attractors is largely similar to that of bodies around black holes. It is currently a very complex and active field of research involving magnetic fields and plasma physics to disentangle what is going on. 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 emission as the kinetic energy of the matter is thermalized. In addition thermonuclear "burning" may occur on the surface of compact massive objects as material collides or builds up. These processes produce irregular intense flares of X-rays and other hard radiation around some objects. The lack of such flare-ups around such a compact concentration of mass is taken as evidence suggesting that the object is a black hole which lacks a surface onto which matter can collect and from which radiation can be emitted.
[edit] Suspected black holes
There is now a great deal 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.
Additionally, there is 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).
Candidates for 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); short duration GRBs are believed to be caused by colliding neutron stars, which form a black hole on merging. Observations of long GRBs in association with supernovae[9] suggest that long GRBs are caused by collapsars;[10] a massive star whose core collapses to form a black hole, drawing in the surrounding material. Therefore, a GRB could possibly signal the birth of a new black hole, aiding efforts to search for them.
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 centre, it is now believed that such supermassive black holes exist in the centre of most galaxies, including our own Milky Way. Sagittarius A* is now generally agreed to be the location of a supermassive black hole at the centre of the Milky Way galaxy. The orbits of stars within a few AU of Sagittarius A* rule out any object other than a black hole at the centre of the Milky Way assuming the current standard laws of physics are correct.
The current picture is that all galaxies may have a supermassive black hole in their centre, and that this black hole accretes 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 may also explain why there are no nearby quasars.
Although 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.
In 2002, the Hubble Telescope identified evidence indicating that intermediate size black holes exist in globular clusters named M15 and G1. The evidence for the black holes stemmed from the orbital velocity of the stars in the globular clusters; however, a group of neutron stars could cause similar observations.
[edit] Nearest black hole candidates
Apart from Sagittarius A*, the black hole in our Milky Way's center, there are several strong black hole candidates nearer than it to us, all of them X-ray binaries which draw matter from their partner via an accretion disk. They have masses from three to more than a dozen sun masses.[11][12]
| Name | Mass in M☉ | Mass of partner (M☉) | Orbital period (days) | Distance from Earth (light years) |
|---|---|---|---|---|
| A0620-00 | 9−13 | 2.6−2.8 | 0.33 | ~3500 |
| GRO J1655-40 | 6−6.5 | 2,6−2,8 | 2.8 | 5000−10000 |
| XTE J1118+480 | 6.4−7.2 | 6−6.5 | 0.17 | 6200 |
| Cyg X-1 | 7−13 | 0.25 | 5.6 | 6000−8000 |
| GRO J0422+32 | 3−5 | 1.1 | 0.21 | ~8500 |
| GS 2000+25 | 7−8 | 4.9−5.1 | 0.35 | ~8800 |
| V404 Cyg | 10−14 | 6.0 | 6.5 | ~10000 |
| GX 339-4 | 5−6 | 1.75 | ~15000 | |
| GRS 1124-683 | 6.5−8.2 | 0.43 | ~17000 | |
| XTE J1550-564 | 10−11 | 6.0−7.5 | 1.5 | ~17000 |
| XTE J1819-254 | 10−18 | ~3 | 2.8 | < 25000 |
| 4U 1543-475 | 8−10 | 0.25 | 1.1 | ~24000 |
| 1915+105 GRO | . | . | . | . |
| Sgr A* | 3.7 million | − | − | ~25000 |
[edit] Recent discoveries
In 2004, astronomers found 31 candidate 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.[13]
In June 2004 astronomers 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 rapid creation of super-massive black holes in the early universe.[14]
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.[15][16] This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.
In February 2005, a blue giant star SDSS J090745.0+24507 was found to be leaving the Milky Way at twice the escape velocity (0.0022 of the speed of light), having been catapulted out of the galactic core which its path can be traced back to. The high velocity of this star supports the hypothesis of a super-massive black hole in the centre of the galaxy.
The formation of micro black holes on Earth in particle accelerators has been tentatively reported,[17] but not yet confirmed. So far there are no observed candidates for primordial black holes.
In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole inside a compact group of ancient stars known as a globular cluster. Many doubted newly-formed black holes could exist in such locations due to gravitational interactions.[18]
[edit] Features and theories
Black holes require the general relativistic concept of a curved spacetime: their most striking properties rely on a distortion of the geometry of the space surrounding them.
[edit] Gravitational field
The gravitational field outside a black hole is identical to the field produced by any other spherically symmetric object of the same mass. The popular conception of black holes as "sucking" things in is false: objects can orbit around black holes indefinitely without getting any closer. The strange properties of spacetime only become noticeable closer to the black hole.
[edit] Event horizon
The effective boundary of a black hole is known as the event horizon. The event horizon is not a physical surface; it is the invisible dividing line in space beyond which outside observers cannot see, and from within which matter and energy cannot exit. Stephen Hawking proved that the topology of the event horizon of a non-spinning black hole is a sphere. Due to the extremely strong gravitational field, anything inside the event horizon, including a photon, is prevented from escaping across the event horizon. Particles from outside this region can fall in, cross the event horizon, and will never be able to leave. In this sense, the event horizon is a little like the point of no return.
External observers cannot probe the interior of a black hole. Consequently according to (non-quantum) general relativity, black holes can be entirely characterized by these parameters: energy, linear momentum, angular momentum, electric charge, and position at a specific time. This principle is summarized by the saying, coined by John Archibald Wheeler, "black holes have no hair" meaning that there are no features that distinguish one black hole from another, other than energy, linear momentum, charge, angular momentum, and location.
[edit] Space-time distortion and frame of reference
Objects in a gravitational field experience a slowing down of time, called time dilation, relative to observers outside the field. This phenomenon has been verified experimentally in the Scout rocket experiment of 1976,[19] and is, for example, taken into account in the Global Positioning System (GPS). 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. As the object falls into the black hole, it appears redder and dimmer to the distant observer, due to 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.
From the viewpoint of the falling object, nothing particularly special happens at the event horizon. The object crosses the event horizon and reaches the singularity at the center within a finite amount of proper time, as measured by a watch carried with the falling observer.
From the viewpoint of the falling observer, distant objects may appear either blue-shifted or red-shifted, depending on the observer'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] Inside the event horizon
Space-time inside the event horizon of an uncharged non-rotating black hole is peculiar in that the singularity is in every observer's future, so all particles within the event horizon move inexorably towards it (Penrose and Hawking). This means that there is a conceptual inaccuracy in the non-relativistic concept of a black hole as originally proposed by John Michell in 1783. In Michell's theory, the escape velocity at the surface of the star is greater than the speed of light, but it would still 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 line comes back out through the event horizon. Once inside the black hole, at most one course-correction (performed immediately) is appropriate to maximize your survival time.
As the object continues to approach the singularity, it will be stretched radially with respect to the black hole and compressed in directions perpendicular to this axis. This phenomenon, called spaghettification, occurs as a result of tidal forces: the parts of the object closer to the singularity feel a stronger pull towards it (causing stretching along the axis), and all parts are pulled in the direction of the singularity, which is only aligned with the object's average motion along the axis of the object (causing compression towards the axis).
[edit] Singularity
At the center of the black hole, well inside the event horizon, general relativity predicts a singularity, a place where the curvature of spacetime becomes infinite and gravitational forces become infinitely strong.
In a non-rotating black hole, the singularity is one-dimensional, extended in the time direction only. In a rotating black hole, the singularity is two-dimensional, extended in time and in longitude.
It is expected that future refinements or generalizations 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.[20]
The cosmic censorship hypothesis asserts that there are no naked singularities in general relativity. This hypothesis is that every singularity is hidden behind an event horizon and cannot be probed. Whether this hypothesis is true remains an active area of theoretical research.
[edit] Rotating black holes
According to theory, the event horizon of a black hole that is not spinning is spherical, and its singularity is expected to be a single point where the curvature becomes infinite. 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 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 Greek name ergosphere ("sphere of work") because it is capable of doing work.
The singularity inside a rotating black hole is expected to be a ring, rather than a point, though the interior geometry of a rotating black hole is currently not well understood. While the fate of an observer falling into a non-rotating black hole is spaghettification, the fate of an observer falling into a rotating black hole is much less clear. For instance, in the Kerr geometry, an infalling observer can potentially escape spaghettification by passing through an inner horizon. However, it is unlikely that the actual interior geometry of a rotating black hole is the Kerr geometry due to stability issues, and the ultimate fate of an observer falling into a rotating black hole is currently not known.[21]
[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.
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.[22] 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 3rG. The location of the marginally stable orbit, thought to be close to the inner edge of an accretion disk, is at 6rG for a Schwarzschild black hole.
[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.[23][24]
Among the alternate models are magnetospheric eternally collapsing objects, clusters of elementary particles[25] (e.g., boson stars[26]), fermion balls,[27] self-gravitating, degenerate heavy neutrinos[28] and even clusters of very low mass (~0.04 solar mass) black holes.[25]
[edit] Black holes and Earth
Black holes are sometimes listed among the most serious potential threats to Earth and humanity.[29][30]There are two principal ways in which they could affect Earth.
- There is evidence that some black holes are not stationary, rather, they "wander" through space.[31] There is only a very slim possibility that a rogue black hole might pass near, or even through our Solar System.[32] At a typical speed of stars' relative motion in the Milky Way, it would take a few decades for a black hole to traverse the Solar System, during which time it would wreak havoc on planets' orbits, and possibly affect Earth and Sun directly if it passes near them.
- There is a theoretical possibility that a micro black hole might be created inside a particle accelerator.[33] 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 this way, it is likely that they are already created every day without our involvement.
Even if, say, two protons at the Large Hadron Collider can 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 Hawking formula gives 10-100 seconds.
