In
general relativity, a
black hole is a region of space in which the
gravity well is so deep that
gravitational time dilation
halts time completely. This forms an
event
horizon, a one-way surface into which objects can fall, but out
of which nothing can appear. It is called "black" because it
absorbs all the light that hits it, reflecting nothing, just like a
perfect
black body in
thermodynamics. Quantum analysis of black
holes shows them to possess a
temperature and
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 which looks empty. Alternatively, one can see gas
falling into a relatively small black hole, from a companion star.
This gas spirals inward, heating up to very high temperatures and
emitting large amounts of radiation that can be detected from
earthbound and earth-orbiting telescopes. Such observations have
resulted in the scientific consensus that, barring a breakdown in
our understanding of nature, black holes exist in our
universe.
History
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:
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). 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, 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. 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 briefly known as
"frozen stars," 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
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". 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, 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:
Properties and structure
The
No hair theorem states that,
once it achieves a stable condition after formation, a black hole
has only three independent physical properties: mass, charge, and
angular momentum. Any two black holes that share the same values
for these properties, or parameters, are classically
indistinguishable.
These properties are special because they are visible from outside
the black hole. For example, a charged black hole repels other like
charges just like any other charged object, despite the fact that
photons, the particles responsible for electric and magnetic
forces, cannot escape from the interior region. The reason is
Gauss's law, the total electric flux
going out of a big sphere always stays the same, and measures the
total charge inside the sphere. When charge falls into a black
hole, electric field lines still remain, poking out of the horizon,
and these field lines conserve the total charge of all the
infalling matter. The electric field lines eventually spread out
evenly over the surface of the black hole, forming a uniform
field-line density on the surface. The black hole acts in this
regard like a classical conducting sphere with a definite
resistivity. Similarly, the total mass inside a sphere containing a
black hole can be found by using the gravitational analog of
Gauss's law, far away from the black hole. Likewise, the angular
momentum can be measured from far away using
frame dragging by the gravitomagnetic
field.
When a black hole swallows any form of matter, its horizon
oscillates like a stretchy membrane with friction, a
dissipative system, until it reaches a
simple final state. This is different from other field theories
like electromagnetism or gauge theory, which never have any
friction or resistivity, because they are time reversible. Because
the black hole eventually achieves a stable state with only three
parameters, there is no way to avoid losing information about the
initial conditions: The gravitational and electric fields of the
black hole give very little information about what went in. The
information that is lost includes every quantity that cannot be
measured far away from the black hole horizon, including the total
baryon number,
lepton number, and all the other nearly
conserved pseudo-charges of particle physics. This behavior is so
puzzling, that it has been called the
black hole information loss
paradox.
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 hole after the
physicist
Karl Schwarzschild who
discovered this
solution in 1915.
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. 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.
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. This is supported by numerical simulations.
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
appears to have an angular momentum near the maximum allowed
value.
By mass
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, including the Milky Way. 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.
- Intermediate –
contain thousands of solar masses. They have been proposed as a
possible power source for ultraluminous X-ray sources.
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. 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.
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. 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. 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. 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.
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. 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. 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.
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. This means that a black hole's mass becomes entirely
compressed into a region with zero volume. 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. 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. 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.
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. 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
ergosphere of a rotating black
hole
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.
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.
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, 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. 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
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. 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. 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 (~10
^{19} GeV/c
^{2} = ~2 × 10
^{-8} kg), where
quantum effects are expected to make the theory of general
relativity break down completely. 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/c
^{2}.
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.
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
In 1974,
Stephen Hawking showed that
black holes are not entirely black but emit small amounts of
thermal radiation. 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. 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 =
mc^{2}). 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/
c^{2} 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.
Observation
Accretion disks and gas jets
Most
accretion disks and
gas jets are not clear proof that a
stellar-mass black hole is
present, because other massive, ultra-dense objects such as
neutron stars and
white dwarfs cause accretion disks and gas jets
to form and to behave in the same ways as those around black holes.
But they can often help by telling astronomers where it might be
worth looking for a black hole.
On the other hand, extremely large accretion disks and gas jets may
be good evidence for the presence of
supermassive black holes, because as
far as we know any mass large enough to power these phenomena must
be a black hole.
Strong radiation emissions
Steady
X-ray and
gamma
ray emissions also do not prove that a black hole is present,
but can tell astronomers where it might be worth looking for one -
and they have the advantage that they pass fairly easily through
nebulae and gas clouds.
But strong, irregular emissions of
X-rays,
gamma rays and other
electromagnetic radiation can help
to prove that a massive, ultra-dense object is
not a black
hole, so that "black hole hunters" can move on to some other
object. Neutron stars and other very dense stars have surfaces, and
matter colliding with the surface at a high percentage of the speed
of light will produce intense flares of radiation at irregular
intervals. Black holes have no material surface, so the absence of
irregular flares around a massive, ultra-dense object suggests that
there is a good chance of finding a black hole there.
Intense but one-time
gamma ray
bursts (GRBs) may signal the birth of "new" black holes,
because astrophysicists think that GRBs are caused either by the
gravitational collapse of
giant stars or by collisions between neutron stars, 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, 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 so the black holes associated with them are actually
billions of years old.
It has been suggested that some
ultraluminous X-ray sources may
be the
accretion disks of
intermediate-mass black
holes.
Quasars are thought to be the accretion
disks of
supermassive black
holes, since no other known object is powerful enough to
produce such strong emissions. Quasars produce strong emission
across the
electromagnetic
spectrum, including
UV,
X-rays and
gamma-rays and
are visible at tremendous distances due to their high
luminosity. Between 5 and 25% of quasars are
"radio loud," so called because of their powerful
radio emission.
Gravitational lensing
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.
Orbiting objects
Objects orbiting black holes probe the gravitational field around
the central object. An early example, discovered in the 1970s, is
the accretion disk orbiting the putative black hole responsible for
Cygnus X-1, a famous X-ray source. While
the material itself cannot be seen directly, the X rays flicker on
a millisecond time scale, as expected for hot clumpy material
orbiting a ~10 solar-mass black hole just prior to accretion. The
X-ray spectrum exhibits the characteristic shape expected for a
disk of orbiting relativistic material, with an iron line, emitted
at ~6.4 keV, broadened to the red (on the receding side of the
disk) and to the blue (on the approaching side).
Another example is the
star S2, seen
orbiting the
Galactic center. Here
the star is several light hours from the ~3.5×10
^{6} solar
mass black hole, so its orbital motion can be plotted. Nothing is
observed at the center of the observed orbit, the position of the
black hole itself—as expected for a black object.
Determining the mass of black holes
Quasi-periodic
oscillations can be used to determine the mass of black holes.
The technique uses a relationship between black holes and the inner
part of their surrounding disks, where gas spirals inward before
reaching the event horizon. As the gas collapses inwards, it
radiates X-rays with an intensity that varies in a pattern that
repeats itself over a nearly regular interval. This signal is the
Quasi-Periodic Oscillation, or QPO. A QPO’s frequency depends on
the black hole’s mass; the event horizon lies close in for small
black holes, so the QPO has a higher frequency. For black holes
with a larger mass, the event horizon is farther out, so the QPO
frequency is lower.
Black hole candidates
Supermassive
It is now widely accepted that the center of every or at least
nearly every galaxy contains a supermassive black hole. The close
observational correlation between the mass of this hole and the
velocity dispersion of the host galaxy's bulge, known as the
M-sigma relation, strongly suggests
a connection between the formation of the black hole and the galaxy
itself.
For decades, astronomers have used the term "
active galaxy" to describe galaxies with
unusual characteristics, such as unusual
spectral line emission and very strong
radio emission. However, theoretical and
observational studies have shown that the
active galactic nuclei (AGN) in
these galaxies may contain
supermassive black holes. The
models of these AGN consist of a central black hole that may be
millions or billions of times more massive than the
Sun; a disk of
gas and
dust called an
accretion disk; and two
jets that are perpendicular to the
accretion disk.
Although supermassive black holes are expected to be found in most
AGN, only some galaxies' nuclei have been more carefully studied in
attempts to both identify and measure the actual masses of the
central supermassive black hole candidates. Some of the most
notable galaxies with supermassive black hole candidates include
the
Andromeda Galaxy,
M32,
M87,
NGC 3115,
NGC 3377,
NGC 4258, and the
Sombrero Galaxy.
Astronomers are confident that our own
Milky
Way galaxy has a supermassive black hole at its center, in a
region called
Sagittarius A* since:
- * A star called S2 follows an elliptical orbit with a period of 15.2 years and a pericenter (closest) distance of 17 light hours from the central object.
- * The first estimates indicated that the central object
contains 2.6 million solar masses and has a radius of less than 17
light hours. Only a black hole can contain such a vast mass in such
a small volume.
- * Further observations strengthened the case for a black hole,
by showing that the central object's mass is about 3.7 million
solar masses and its radius no more than 6.25 light-hours.
Intermediate-mass
In 2002, the Hubble Space Telescope produced observations
indicating that
globular clusters
named
M15 and
G1
may contain
intermediate-mass black holes.
This interpretation is based on the sizes and periods of the orbits
of the stars in the globular clusters. But the Hubble evidence is
not conclusive, since a group of
neutron
stars could cause similar observations. Until recent
discoveries, many astronomers thought that the complex
gravitational interactions in globular clusters would eject
newly-formed black holes.
In November 2004 a team of astronomers reported the discovery of
the first well-confirmed
intermediate-mass black hole in
our Galaxy, orbiting three light-years from Sagittarius A*. This
black hole of 1,300 solar masses is within a cluster of seven
stars, possibly the remnant of a massive star cluster that has been
stripped down by the Galactic Centre. This observation may add
support to the idea that supermassive black holes grow by absorbing
nearby smaller black holes and stars.
In January 2007, researchers at the University of Southampton in
the United Kingdom reported finding a black hole, possibly of about
10 solar masses, in a globular cluster associated with a galaxy
named NGC 4472, some 55 million light-years away.
Stellar-mass
The Milky Way galaxy contains several probable
stellar-mass black holes which are
closer to Earth than the supermassive black hole in the
Sagittarius A* region. These candidates are
all members of
X-ray binary systems in
which the denser object draws matter from its partner via an
accretion disk. The probable black holes in these pairs range from
three to more than a dozen
solar masses.
The most distant stellar-mass black hole ever observed is a member
of a binary system located in the
Messier
33 galaxy.
Micro
There is theoretically no smallest size for a black hole. Once
created, it has the properties of a black hole.
Stephen Hawking theorized that
primordial black holes could evaporate
and become even tinier, i.e.
micro
black holes. Searches for evaporating primordial black holes
are proposed for the
Fermi Gamma-ray Space
Telescope, which was launched on June 11, 2008. However, if
micro black holes can be created by other means, such as by cosmic
ray impacts or in colliders, that does not imply that they must
evaporate.
The formation of black hole analogs on Earth in
particle accelerators has been
reported. These black hole analogs are not the same as
gravitational black holes, but they are vital testing grounds for
quantum theories of gravity.
They act like black holes because of the
correspondence between the theory of
the strong nuclear force, which has nothing to do with gravity, and
the quantum theory of gravity. They are similar because both are
described by
string theory. So the
formation and disintegration of a
fireball in quark gluon plasma can be
interpreted in black hole language.
The fireball at the Relativistic Heavy Ion Collider [RHIC] is a phenomenon which is closely analogous
to a black hole, and many of its physical properties can be
correctly predicted using this analogy. The fireball,
however, is not a gravitational object.
It is presently
unknown whether the much more energetic Large Hadron Collider [LHC] would be capable of producing the speculative
large extra dimension micro black hole, as many theorists have
suggested. See
Safety
of particle collisions at the Large Hadron Collider for a more
in depth discussion.
Open questions
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, even if they collide and swallow
each other; that is merge. 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
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).
Fuzzballs
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.
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.
See also
References
- Thermodynamics of Black Holes,P.C.W Davies,
Rep. Prog. Phys Vol. 41(1978),
pp.1313-1355.
- Laplace; see Israel, Werner (1987), "Dark stars: the evolution
of an idea", in Hawking, Stephen W. & Israel, Werner, 300 Years
of Gravitation, Cambridge University Press, Sec. 7.4
- On Massive Neutron Cores, J. R. Oppenheimer and
G. M. Volkoff, Physical Review 55, #374
(15 February 1939), pp. 374–381.
- D. Finkelstein (1958). "Past-Future Asymmetry of the
Gravitational Field of a Point Particle". Phys. Rev. 110:
965–967.
- Thorne, "Black Holes, The Membrane Paradigm"
- John Preskill(1994)" Black holes and information: A crisis in quantum
physics"
- Daniel Carmody(2008)" The Fate of Quantum Information in a Black Hole"
- and .
- For a review see .
- For a discussion of these numerical simulations see .
- .
- Citation: AdS/CFT duality and the black hole information
paradox, SD Mathur and Oleg Lunin, Nuclear
Physics B, 623, (2002), ( arxiv);
Statistical interpretation of Bekenstein entropy for systems
with a stretched horizon, SD Mathur and Oleg Lunin,
Physics Review Letters, 88 (2002) ( arxiv);
and correspondence between Dr. Mathur and Wikipedia, as
documented on .
Further reading
Popular reading
University textbooks and monographs
- , the lecture notes on which the book was based are available
for free from Sean Carroll's website.
- .
- .
- .
- .
- .
- .
- .
- .
Research papers
- Stephen Hawking's purported solution to the black hole unitarity paradox, first reported at a conference
in July 2004.
- More accurate mass and position for the black hole at the
centre of the Milky Way.
- Lecture notes from 2005 SLAC Summer
Institute.
External links