Black hole: 2009

Thursday, December 10, 2009

Black hole

Simulated view of a black hole in front of the Large Magellanic Cloud. The ratio between the black hole Schwarzschild radius and the observer distance to it is 1:9. Of note is the gravitational lensing effect known as an Einstein ring, which produces a set of two fairly bright and large but highly distorted images of the Cloud as compared to its actual angular size.

According to the general theory of relativity, a black hole is a region of space from which nothing, including light, can escape. It is the result of the deformation of spacetime caused by a very compact mass. Around a black hole there is an undetectable surface which marks the point of no return, called an event horizon. It is called "black" because it absorbs all the light that comes towards it, reflecting nothing, just like a perfect black body in thermodynamics.^[1] Under the theory of quantum mechanics black holes possess a temperature and emit Hawking radiation.

Despite its invisible interior, a black hole can be observed through its interaction with other matter. A black hole can be inferred by tracking the movement of a group of stars that orbit a region in space. Alternatively, when gas falls into a stellar black hole from a companion star, the gas spirals inward, heating to very high temperatures and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes.

Astronomers have identified numerous stellar black hole candidates, and have also found evidence of supermassive black holes at the center of galaxies. After observing the motion of nearby stars for 16 years, in 2008 astronomers found compelling evidence that a supermassive black hole of more than 4 million solar masses is located near the Sagittarius A* region in the center of our own Milky Way galaxy.

History

Simulation of Gravitational lensing by a black hole which distorts the image of a galaxy in the background. (Click for larger animation.)

The idea of a body so massive that even light could not escape was put forward by geologist John Michell in a letter written to Henry Cavendish in 1783 to the Royal Society:

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, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity.

—John Michell^[2]

In 1796, 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).^[3]^[4] Such "dark stars" were largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity. Unlike the modern black hole concept, the object behind the horizon of a dark star is assumed to be stable against collapse.

General Relativity

In 1915, Albert Einstein developed his general theory of relativity, having earlier shown that gravity does in fact influence light's motion. A few months later, Karl Schwarzschild gave the solution for the gravitational field of a point mass and a spherical mass,^[5] 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 Hendrik Lorentz, independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties. In 1930, astrophysicist Subrahmanyan Chandrasekhar calculated, using general relativity, that a non-rotating body of electron-degenerate matter above 1.44 solar masses (the Chandrasekhar limit) would collapse. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Eddington was partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star, which is itself stable because of the Pauli exclusion principle. But in 1939, Robert Oppenheimer and others predicted that stars above approximately three solar masses (the Tolman-Oppenheimer-Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar.^[6] Oppenheimer and his co-authors used Schwarzschild's system of coordinates (the only coordinates available in 1939), which produced mathematical singularities at the Schwarzschild radius, in other words some of the terms in the equations became infinite at the Schwarzschild radius. This was interpreted as indicating that the Schwarzschild radius was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called "frozen stars,"^[7] because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius. This is a known property of modern black holes, but it must be emphasized that the light from the surface of the frozen star becomes redshifted very fast, turning the black hole black very quickly. Many physicists could not accept the idea of time standing still at the Schwarzschild radius, and there was little interest in the subject for over 20 years.

Golden age

See also: golden age of general relativity

In 1958, David Finkelstein introduced the concept of the event horizon by presenting Eddington-Finkelstein coordinates, which enabled him to show that "The Schwarzschild surface r = 2 m is not a singularity, but that it acts as a perfect unidirectional membrane: causal influences can cross it in only one direction".^[8] This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. All theories up to this point, including Finkelstein's, covered only non-rotating black holes. In 1963, Roy Kerr found the exact solution for a rotating black hole. The rotating singularity of this solution was a ring, and not a point. A short while later, Roger Penrose was able to prove that singularities occur inside any black hole. In 1967, astronomers discovered pulsars,^[9]^[10] 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 objects that might be formed by gravitational collapse.

Physicist John Wheeler is widely credited with coining the term black hole in his 1967 public lecture Our Universe: the Known and Unknown, as an alternative to the more cumbersome "gravitationally completely collapsed star." However, Wheeler insisted that someone else at the conference had coined the term and he had merely adopted it as useful shorthand. The term was also cited in a 1964 letter by Anne Ewing to the AAAS:

According to Einstein’s general theory of relativity, as mass is added to a degenerate star a sudden collapse will take place and the intense gravitational field of the star will close in on itself. Such a star then forms a "black hole" in the universe.

—Ann Ewing, letter to AAAS^[11]

Properties and structure

Classification

By physical properties

The simplest black hole has mass but neither charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after the physicist Karl Schwarzschild who discovered this solution in 1915.^[5] It was the first non-trivial exact solution to the Einstein field equations to be discovered, and according to Birkhoff's theorem, the only vacuum solution that is spherically symmetric.^[17] This means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near the black hole horizon; far away, the external gravitational field is identical to that of any other body of the same mass.^[18]

More general black hole solutions were discovered later in the 20th century. The Reissner-Nordström metric describes a black hole with electric charge, while the Kerr metric yields a rotating black hole. The more generally known stationary black hole solution, the Kerr-Newman metric, describes both charge and angular momentum.

While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In natural units , the total charge $Q\,$ and the total angular momentum $J\,$ are expected to satisfy

$Q^2+\left ( \tfrac{J}{M} \right )^2\le M^2\,$

for a black hole of mass M.

Black holes saturating this inequality are called extremal. Solutions of Einstein's equations violating the inequality do exist, but do not have a horizon. These solutions have naked singularities and are deemed unphysical, as the cosmic censorship hypothesis rules out such singularities due to the generic gravitational collapse of realistic matter.^[19] This is supported by numerical simulations.^[20]

Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects, and the black-hole candidate binary X-ray source GRS 1915+105^[21] appears to have an angular momentum near the maximum allowed value.

By mass

Class	Mass	Size
Supermassive black hole	~10⁵–10⁹ M_Sun	~0.001–10 AU
Intermediate-mass black hole	~10³ M_Sun	~10³ km = R_Earth
Stellar-mass	~10 M_Sun	~30 km
Micro black hole	up to ~M_Moon	up to ~0.1 mm

Black holes are commonly classified according to their mass, independent of angular momentum $J\,$ . The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass $M\,$ through

$r_{sh} \approx 2.95\, M/M_\bigodot \;\mathrm{km,}$

where $r_{sh}\,$ is the Schwarzschild radius and $M_\bigodot$ is the mass of the Sun. A black hole's size and mass are thus simply related independent of rotation. According to this criterion, black holes are classed as:

Supermassive – contain hundreds of thousands to billions of solar masses, and are thought to exist in the center of most galaxies,^[22]^[23] including the Milky Way.^[24] They are thought to be responsible for active galactic nuclei, and presumably form either from the coalescence of smaller black holes, or by the accretion of stars and gas onto them. The largest known supermassive black hole is located in OJ 287 weighing in at 18 billion solar masses.^[25]

Intermediate – contain thousands of solar masses. They have been proposed as a possible power source for ultraluminous X-ray sources.^[26] There is no known mechanism for them to form directly, so they likely form via collisions of lower mass black holes, either in the dense stellar cores of globular clusters or galaxies.^{[citation needed]} Such creation events should produce intense bursts of gravitational waves, which may be observed soon. The boundary between super- and intermediate-mass black holes is a matter of convention. Their lower mass limit, the maximum mass for direct formation of a single black hole from collapse of a massive star, is poorly known at present, but is thought to be somewhere well below 200 solar masses.

Stellar-mass – have masses ranging from a lower limit of about 1.4–3 solar masses (1.4 is the Chandrasekhar limit and 3 is the Tolman-Oppenheimer-Volkoff limit for the maximum mass of neutron stars) up to perhaps 15–20 solar masses. They are created by the collapse of individual stars, or by the coalescence (inevitable, due to gravitational radiation) of binary neutron stars. Stars may form with initial masses up to about 100 solar masses, or in the distant past, possibly even higher, but these shed most of their outer massive layers during earlier phases of their evolution, either blown away in stellar winds during the red giant, AGB, and Wolf-Rayet stages, or expelled in supernova explosions for stars that turn into neutron stars or black holes. Being known mostly by theoretical models for late-stage stellar evolution, the upper limit for the mass of stellar-mass black holes is somewhat uncertain at present. The cores of still lighter stars form white dwarfs.

Micro – (also mini black holes) have masses much less than that of a star. At these sizes, quantum mechanics is expected to take effect. There is no known mechanism for them to form via normal processes of stellar evolution, but certain inflationary scenarios predict their production during the early stages of the evolution of the universe.^{[citation needed]} According to some theories of quantum gravity they may also be produced in the highly energetic reaction produced by cosmic rays hitting the atmosphere or even in particle accelerators such as the Large Hadron Collider.^{[citation needed]} The theory of Hawking radiation predicts that such black holes will evaporate in bright flashes of gamma radiation. NASA's Fermi Gamma-ray Space Telescope satellite (formerly GLAST) launched in 2008 is searching for such flashes.^[27]

Event horizon

Main article: Event horizon

Far away from the black hole a particle can move in any direction. It is only restricted by the speed of light.
Closer to the black hole spacetime starts to deform. There are more paths going towards the black hole than paths moving away.
Inside of the event horizon all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape.

The defining feature of a black hole is the appearance of an event horizon; a boundary in spacetime beyond which events cannot affect an outside observer. As predicted by general relativity, the presence of a mass deforms spacetime in such a way that the paths particles take tend towards the mass. At the event horizon of a black hole this deformation becomes so strong that there are no more paths that lead away from the black hole.^[28] Once a particle is inside the horizon, moving into the hole is as inevitable as moving forward in time (and can actually be thought of as equivalent to doing so).

To a distant observer clocks near a black hole appear to tick more slowly than those further away from the black hole.^[29] Due to this effect (known as gravitational time dilation) the distant observer will see an object falling into a black hole slow down as it approaches the event horizon, taking an infinite time to reach it.^[30] At the same time all processes on this object slow down causing emitted light to appear redder and dimmer, an effect known as gravitational red shift.^[31] Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon.

For a non rotating (static) black hole, the Schwarzschild radius delimits a spherical event horizon. The Schwarzschild radius of an object is proportional to the mass.^[32] Rotating black holes have distorted, nonspherical event horizons. Since the event horizon is not a material surface but rather merely a mathematically defined demarcation boundary, nothing prevents matter or radiation from entering a black hole, only from exiting one. The description of black holes given by general relativity is known to be an approximation, and it is expected that quantum gravity effects become significant near the vicinity of the event horizon.^[33] This allows observations of matter in the vicinity of a black hole's event horizon to be used to indirectly study general relativity and proposed extensions to it.

Though black holes themselves may not radiate energy, electromagnetic radiation and matter particles may be radiated from just outside the event horizon via Hawking radiation.^[34]

Singularity

Main article: Gravitational singularity

At the center of a black hole lies the singularity, where matter is crushed to infinite density, the pull of gravity is infinitely strong, and spacetime has infinite curvature.^[35] This means that a black hole's mass becomes entirely compressed into a region with zero volume.^[36] This zero-volume, infinitely dense region at the center of a black hole is called a gravitational singularity.

The singularity of a non-rotating black hole has zero length, width, and height; a rotating black hole is smeared out to form a ring shape lying in the plane of rotation.^[37] The ring still has no thickness and hence no volume.

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.^[38] This breakdown, however, is expected; it occurs in a situation where quantum mechanical effects should describe these actions due to the extremely high density and therefore particle interactions. To date it has not been possible to combine quantum and gravitational effects into a single theory. It is generally expected that a theory of quantum gravity will feature black holes without singularities.^[39]^[40]

Photon sphere

Main article: Photon sphere

The 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 the Schwarzschild radius. The orbits are dynamically unstable, hence any small perturbation (such as a particle of infalling matter) will grow over time, either setting it on an outward trajectory escaping the black hole or on an inward spiral eventually crossing the event horizon.

While light can still escape from inside the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light reaching an outside observer from inside the photon sphere must have been emitted by objects inside the photon sphere but still outside of the event horizon.

Other compact objects, such as neutron stars, can also have photon spheres.^[41] This follows from the fact that the gravitational field of an object does not depend on its actual size, hence any object that is smaller than 1.5 times the Schwarzschild radius corresponding to its mass will indeed have a photon sphere.

Ergosphere

Main article: Ergosphere

The ergosphere is an oblate spheroid region outside of the event horizon, where objects cannot remain stationary.

Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole this effect becomes so strong near the event horizon that an object would have to move faster than the speed of light in the opposite direction to just stand still.^[42]

The ergosphere of a black hole is bounded by, the (outer) event horizon on the inside and an oblate spheroid, which coincides with the event horizon at the poles and is noticeably wider around the equator. The outer boundary is sometimes called the ergosurface.

Objects and radiation can escape normally from the ergosphere. In fact through the Penrose process objects can emerge from the ergosphere with more energy than they entered. This energy is taken from the rotational energy of the black hole causing it to slow down

Formation and evolution

Considering the exotic nature of black holes, it may be natural to question if such bizarre objects could actually exist in nature or to suggest that they are merely pathological solutions to Einstein's equations. Einstein himself wrongly thought that black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius.^[44] This led the general relativity community to dismiss all results to the contrary for many years. However, a minority of relativists continued to contend that black holes were physical objects,^[45] and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to forming an event horizon.

Once an event horizon forms, Roger Penrose proved that a singularity will form somewhere inside it. Shortly afterwards, Stephen Hawking showed that many cosmological solutions describing the big bang have singularities, in the absence of scalar fields or other exotic matter (see Penrose-Hawking singularity theorems). The Kerr solution, the no-hair theorem and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research.^[46] The primary formation process for black holes is expected to be the gravitational collapse of heavy objects such as stars, but there are also more exotic processes that can lead to the production of black holes.

Gravitational collapse

Main article: Gravitational collapse

Gravitational collapse occurs when an object's internal pressure is insufficient to resist the object's own gravity. For stars 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 (the ideal gas law explains the connection between pressure, temperature, and volume).

The collapse may be stopped by the degeneracy pressure of the star's constituents, condensing the matter in an exotic denser state. The result is one of the various types of compact star. Which type of compact star is formed depends on the mass of the remnant - the matter left over after changes triggered by the collapse (such as supernova or pulsations leading to a planetary nebula) have blown away the outer layers. Note that this can be substantially less than the original star - remnants exceeding 5 solar masses are produced by stars which were over 20 solar masses before the collapse.

If the mass of the remnant exceeds ~3-4 solar masses (the Tolman-Oppenheimer-Volkoff limit)—either because the original star was very heavy or because the remnant collected additional mass through accretion of matter—even the degeneracy pressure of neutrons is insufficient to stop the collapse. After this no known mechanism (except possibly quark degeneracy pressure, see quark star) is powerful enough to stop the collapse and the object will inevitably collapse to a black hole.

This gravitational collapse of heavy stars is assumed to be responsible for the formation of most (if not all) stellar mass black holes.

Primordial black holes in The Big Bang

Gravitational collapse requires great densities. In the current epoch of the universe these high densities are only found in stars, but in the early universe shortly after the big bang densities were much greater, possibly allowing for the creation of black holes. The high density alone is not enough to allow the formation of black holes since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to form in such a dense medium, there must be initial density perturbations which can then grow under their own gravity. Different models for the early universe vary widely in their predictions of the size of these perturbations. Various models predict the creation of black holes, ranging from a Planck mass to hundreds of thousands of solar masses.^[47] Primordial black holes could thus account for the creation of any type of black hole.

High energy collisions

A simulated event in the CMS detector, a collision in which a micro black hole may be created.

Gravitational collapse is not the only process that could create black holes. In principle, black holes could also be created in high energy collisions that create sufficient density. However, to date, no such events have ever been detected either directly or indirectly as a deficiency of the mass balance in particle accelerator experiments.^[48] This suggests that there must be a lower limit for the mass of black holes. Theoretically this boundary is expected to lie around the Planck mass (~10¹⁹ GeV/c² = ~2 × 10^-8 kg), where quantum effects are expected to make the theory of general relativity break down completely.^{[citation needed]} This would put the creation of black holes firmly out of reach of any high energy process occurring on or near the Earth. Certain developments in quantum gravity however suggest that this bound could be much lower. Some braneworld scenarios for example put the Planck mass much lower, may be even as low as 1 TeV/c².^[49] This would make it possible for micro black holes to be created in the high energy collisions occurring when cosmic rays hit the Earth's atmosphere, or possibly in the new Large Hadron Collider at CERN. These theories are however very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.^{[citation needed]}

Growth

Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb interstellar dust from its direct surroundings and omnipresent cosmic background radiation, but neither of these processes should significantly affect the mass of a stellar black hole. More significant contributions can occur when the black hole formed in a binary star system. After formation the black hole can then leech significant amounts of matter from its companion.

Much larger contributions can be obtained when a black hole merges with other stars or compact objects. The supermassive black holes suspected in the center of most galaxies are expected to have formed from the coagulation of many smaller objects. The process has also been proposed as the origin of some intermediate-mass black holes.

As an object approaches the event horizon, the horizon near the object bulges up and swallows the object. Shortly thereafter the increase in radius (due to the extra mass) is distributed evenly around the hole.

Evaporation

Main article: Hawking radiation

In 1974, Stephen Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation.^[50] He got this result by applying quantum field theory in a static black hole background. The result of his calculations is that a black hole should emit particles in a perfect black body spectrum. This effect has become known as Hawking radiation. Since Hawking's result, many others have verified the effect through various methods.^[51] If his theory of black hole radiation is correct then black holes are expected to emit a thermal spectrum of radiation, and thereby lose mass, because according to the theory of relativity mass is just highly condensed energy (E = mc²).^[50] Black holes will shrink and evaporate over time. The temperature of this spectrum (Hawking temperature) is proportional to the surface gravity of the black hole, which for a Schwarzschild black hole is inversely proportional to the mass. Large black holes, therefore, emit less radiation than small black holes.

A stellar black hole of 5 solar masses has a Hawking temperature of about 12 nanokelvins. This is far less than the 2.7 K produced by the cosmic microwave background. Stellar mass (and larger) black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and will thus grow instead of shrink. In order to have a Hawking temperature larger than 2.7 K (and be able to evaporate) a black hole needs to be lighter than the Moon (and therefore a diameter of less than a tenth of a millimeter).

On the other hand if a black hole is very small, the radiation effects are expected to become very strong. Even a black hole that is heavy compared to a human would evaporate in an instant. A black hole the weight of a car (~10^-24 m) would only take a nanosecond to evaporate, during which time it would briefly have a luminosity more than 200 times that of the sun. Lighter black holes are expected to evaporate even faster, for example a black hole of mass 1 TeV/c² would take less than 10^-88 seconds to evaporate completely. Of course, for such a small black hole quantum gravitation effects are expected to play an important role and could even – although current developments in quantum gravity do not indicate so – hypothetically make such a small black hole stable.

Observational evidence

By their very nature black holes do not directly emit any signals other than the hypothetical Hawking radiation. Since the Hawking radiation for an astrophysical black holes is predicted to be very weak, this makes it impossible to directly detect astrophysical black holes from the Earth. A possible exception to the Hawking radiation being weak is the last stage of the evaporation of light (primordial) black holes. Searches for such flashes in the past has proven unsuccessful and provides stringent limits on the possibility of existence of light primordial black holes.^[52] NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes.^[53]

Astrophysicists searching for black holes thus have to rely on indirect observations. Using the gravitational interactions between a black hole and its surrounding its it is sometimes possible to infer its existence.

Accretion of matter

X-ray binaries

Quiescence and advection-dominated accretion flow

The faintness of the accretion disc during quiescence is thought to be caused by the flow entering a mode called an advection-dominated accretion flow (ADAF). In this mode, almost all the energy generated by friction in the disc is swept along with the flow instead of radiated away. If this model is correct, then it forms strong qualitative evidence for the presence of an event horizon. Because, if the object at the center of the disc had a solid surface, it would emit large amounts of radiation is the highly energetic gas hits the surface, an effect that is observed for neutron stars in a similar state.^[54]

Quasi-periodic oscillations

Gamma ray bursts

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^[62] or by collisions between neutron stars,^[63] 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,^[64] 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^[65] so the black holes associated with them are actually billions of years old.

Gravitational lensing

Further information: Gravitational lens

A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is bent around a massive object (such as a black hole) between the source object and the observer. The process is known as gravitational lensing, and is one of the predictions of the general theory of relativity. According to this theory, mass warps space-time to create gravitational fields and therefore bend light as a result.

A source image behind the lens may appear as multiple images to the observer. In cases where the source, massive lensing object, and the observer lie in a straight line, the source will appear as a ring behind the massive object.

Gravitational lensing can be caused by objects other than black holes, because any very strong gravitational field will bend light rays. Some of these multiple-image effects are probably produced by distant galaxies.

Galactic Nuclei

Open questions

Entropy and Hawking radiation

Further information: Hawking radiation and Black hole thermodynamics

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.

In 1971, Stephen Hawking showed that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and swallow each other; that is merge.^[72] This is remarkably similar to the Second Law of Thermodynamics, with area playing the role of entropy. As a classical object with zero temperature it was assumed that black holes had zero entropy. If this were the case, the second law of thermodynamics would be violated by entropy-laden matter entering the black hole, 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 seemed simply an analogy, since zero temperature implies infinite changes in entropy with any addition of heat, which implies infinite entropy. However, in 1974, Hawking applied quantum field theory to the curved spacetime around the event horizon and discovered that black holes emit Hawking radiation, a form of thermal radiation, allied to the Unruh effect, which implied they had a positive temperature. This strengthened the analogy being drawn between black hole dynamics and thermodynamics: using the first law of black hole mechanics, it follows that the entropy of a non-rotating 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 possible 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. The more its temperature 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, which 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.

Black hole unitarity

Main article: Black hole information paradox

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 (T-symmetry). Liouville's Theorem dictates conservation of phase space volume, which can be thought of as 'conservation of information', so there is some problem even in classical (non-quantum general relativity) physics. In quantum mechanics, this corresponds to a vital property called unitarity, which has to do with the conservation of probability (It can also be thought of as a conservation of quantum phase space volume as expressed by the density matrix).^[73]

Fuzzballs

Main article: Fuzzball (string theory)

Fuzzballs are theorized by some superstring theory scientists to be the true quantum description of black holes. The theory resolves the information paradox eliminates the need for a singularity at the heart of the black hole with infinite spacetime curvature due to an infinitely intense gravitational field from a region of zero volume. Modern physics breaks down when such parameters are infinite and zero.

Samir Mathur of Ohio State University, with postdoctoral researcher Oleg Lunin, proposed via two papers in 2002 that black holes are actually spheres of strings with a definite volume; they are not a singularity, which the classic view holds to be a zero-dimensional, zero-volume point into which a black hole’s entire mass is concentrated.^[74]

String theory holds that the fundamental constituents of subatomic particles, including the force carriers (e.g., quarks leptons, photons, and gluons), all comprise a one-dimensional string of energy that takes on its identity by vibrating in different modes and/or frequencies. Quite unlike the view of a black hole as a singularity, a small fuzzball can be thought of as an extra-dense neutron star where its neutrons have decomposed, or “melted,” liberating the quarks (strings in string theory) comprising them. Accordingly, fuzzballs can be regarded as the most extreme form of degenerate matter.

Black hole

Thursday, December 10, 2009

Black hole

History

General Relativity

Golden age

Properties and structure

Classification

By physical properties

By mass

Event horizon

Singularity

Photon sphere

Ergosphere

Formation and evolution

Gravitational collapse

Primordial black holes in The Big Bang

High energy collisions

Growth

Evaporation

Observational evidence

Accretion of matter

X-ray binaries

Quiescence and advection-dominated accretion flow

Quasi-periodic oscillations

Gamma ray bursts

Gravitational lensing

Galactic Nuclei

Open questions

Entropy and Hawking radiation

Black hole unitarity

Fuzzballs

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