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A classical black hole is a concentration of mass with a gravitational field so strong that its escape velocity exceeds the speed of light. This implies that light cannot escape its gravity, hence the term black. No matter or information can flow from the interior of a black
hole to an outside observer (e.g. one cannot bring out some of its mass, or light it up with a flashlight). A black hole bears
witness to its existence solely through its strong gravitational field — which makes it behave as "a hole in space".
The term black hole is also used metaphorically to describe any entity (e.g., a project or a
company) that can consume large amounts of something (e.g., money or effort) with little or no return. In programmer's jargon, it is used for a
pipe which feeds into Unix's /dev/null.
History
The concept of a body so massive that not even light could escape from it was put forward by the British geologist Rev. John Mitchell in a 1783 paper sent to the Royal Society. At
that time, the Newtonian theory of gravity and the the concept of escape velocity were well known. Mitchell 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 in the proportion of five hundred to one, and by
supposing light to be attracted by the same force in proportion to its 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, Mitchell considered the possibility that many such objects could be present in the cosmos
without us being able to see them.
In 1796, the French mathematician Pierre 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 emphasis was put on the wave properties of light, which were thought not to be
influenced by gravity.
In 1915 Einstein developed the theory of gravity called General Relativity. Earlier he had shown that gravity does influence
the wave properties of 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 black hole,
but was not well understood at that time. Schwarzschild himself thought it not to be physical.
In 1939 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.
The use of the expression "black hole" for this concept was coined by theoretical physicist John Wheeler in 1967 [1] .
Qualitative physics
A correct understanding of black holes is possible only within the framework of general relativity, which is unfortunately quite counter-intuitive.
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. The event horizon bounds the "interior" if the black hole;
anything there, including photons directed outwards, are prevented from reaching the
event horizon by the strong gravitational field. On the other hand, particles from outside that region can fall in and cross the
event horizon, but 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. Indeed, according to current theory, black holes have no observable external characteristics that can be used to
determine what they are like inside — a principle summarized by the saying "black holes have no hair". Black holes are
completely specified by three measurable parameters: mass, angular momentum, and electric
charge.
Objects in a gravitational field experience time dilation. This slowing down of time, called time dilation, has been verified
experimentally: Scott Rocket Experiment, 1976, http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html.
Near a black hole the time dilation increases very much. It takes forever, as noted by an external observer, for an object to
approach the event horizon.
The singularity
At the center of the event horizon is a singularity, a place where spacetime becomes infinitely curved (i.e., where
gravity becomes infinitely strong, and infinitely varied). 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.
There is a fundamental conflict between general relativity, GR, and quantum mechanics. It is possible that string theory will resolve this conflict. Besides this issue, there is a problem
with the formal equations of GR and the meaning of physics. There is a formal solution to the GR equations for an object crossing
the surface of the black hole and entering it. This is a strange solution due to the inability in principle to observe this.
Mathematically, this solution leads to a singularity at the center of the black hole (Penrose and Hawking http://www.maths.soton.ac.uk/relativity/GRExplorer/singularities/singtheorems.htm).
Actually, the singularity is at the Plank distance from the center.
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 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; but the crossing is not as physically traumatic as one may think. It is true
that once he gets close enough to the singularity, the gravity forces acting on different parts of his body will become so
discrepant that even his atoms will be torn apart. However, 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 himself will not notice anything special when he
crosses the latter. Conversely, for a small black hole, those tidal effects may become fatal well before the astronaut reaches
the event horizon.
Spinning 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 is spinning, its event horizon is predicted have a shape similar to that of an
oblate ellipsoid, a
sphere flattened along one axis; and its singularity will be not a single point but a circle of zero thickness, surrounding the
horizon's center. The spin can be detected from the outside, not only from its "shape" but also from certain relativistic
effects.
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, Bekenstein proposed that the entropy of a black hole really is proportionate 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 proportionate 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 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 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 an instantaneous flash of
radiation. Hence, every black hole that cannot "eat" new mass has a finite life that is directly related to its mass.
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 could 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
gets increasingly deformed. When the escape velocity at a certain distance from the center reaches the speed of light, an event
horizon is formed, and what was a mere "dimple" in space suddenly gives in and becomes a bottomless pit, swallowing all the mass
that was inside the horizon. A crude analogy is dripping honey from a spoon: once the hanging drop grows beyond a certain size,
surface tension "gives", and the drop falls leaving behind a filament of flowing honey.
A quantitative analysis of this idea led to the prediction that a star with about 3 times the mass of the sun will almost
inevitably reach a point in its evolution where, having exhausted
all its nuclear fuel, it will shrink to the critical size needed to undergo gravitational collapse. Once it starts, the collapse
cannot be stopped by any physical force, and a black hole is created. Thus, to the question "do black holes exist", astrophysists
generally answer "most likely" — but admit that no definite proof exists yet.
A few physicists believe that such black holes do not exist, because some process will stop the collapse. However, this
conjecture requires some radically new and untested physics.
Stellar collapse will generate black holes containing at least one or two solar masses. Black holes smaller than this limit
can only be created only 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, creating primordial black holes which could have 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 exists 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 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 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 physics of materials near these non-black hole
objects is largely but not completely identical to the physics of materials around black holes. 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. Its identification as a black hole would have to argue that (1) physics knows of no
other object that could be so massive and compact, and (2) according to general relativity, any concentration of matter that
massive and compact would necessarily collapse into a black hole.
One important 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 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:
- stellar mass black holes with masses of a typical star (4–15 times the mass of our Sun), and
- supermassive black holes with masses perhaps 1%
that of a typical galaxy (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 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 bursters (GRBs), although observations of
GRBs in association with supernova 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.
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, with the metric is
- ,
where relativistic units c = G = 1 are used and 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
-
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, it would have to be compressed a ludicrous 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. The generalization of the Schwarzschild radius is known as the event
horizon.
Recent Discoveries
In 2004 a cluster of black holes was detected, broadening our understanding of the frequency of black holes throughout out
universe. It is now thought that scientists' inferences of how many black holes are in our universe were quite off until now. It
is predicted due to these finds in 2004 that there are close to five fold the number of black holes that there were predicted to
be before this discovery.
Related topics
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