BLACK HOLES AT THE CORES OF GALAXIES
IN THE UNIVERSE
Simulation of gravitational
lensing by a black hole, which distorts
the image of a galaxy in
the background (larger animation)
The Black hole at the core of Milky Way galaxy
Simulated view of a black hole (center) in front of the Large Magellanic Cloud. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the Milky Way disk appears distorted into an arc.
Simulated view of a black hole (center) in front of the Large Magellanic Cloud. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the Milky Way disk appears distorted into an arc.
Introduction
The space-time
The space-time
continuum is a mathematical model that
combines space and time
into a single construct. This space-time is usually explained with a model where space is three-dimensional and
time has the role of the fourth dimension.
If one follows the model of space that Euclid had, our universe has three dimensions of space, and one dimension of time.
By combining space and time into a single manifold,
physicists have simplified a good deal of physical theory, as well as described
in a more uniform way the workings of the universe at both levels: the very
large (supergalactic) and very small (subatomic).
In classical mechanics, the use of space-time over Euclidean
space is optional, as time is independent of mechanical motion in three
dimensions. In relativistic contexts, however, time cannot be separated from
the three dimensions of space as it depends on an object's velocity relative to
the speed of light.
This new reality was that space and time, as physical
constructs, have to be combined into a new mathematical/physical entity called
'space-time', because the equations of relativity show that both the space and
time coordinates of any event must get mixed together by the mathematics, in
order to accurately describe what we see.
Because space consists of 3 dimensions, and time is
1-dimensional, space-time must, therefore, be a 4-dimensional object. It is
believed to be a 'continuum' because so far as we know, there are no missing
points in space or instants in time, and both can be subdivided without any
apparent limit in size or duration. So, physicists now routinely consider our
world to be embedded in this 4-dimensional Space-Time continuum, and all
events, places, moments in history, actions and so on are described in terms of
their location in Space-Time.
Space-time does not evolve, it simply exists. When we
examine a particular object from the stand point of its space-time
representation, every particle is located along its world-line. This is a
spaghetti-like line that stretches from the past to the future showing the
spatial location of the particle at every instant in time. This world-line exists
as a complete object which may be sliced here and there so that you can see
where the particle is located in space at a particular instant. Once you
determine the complete world line of a particle from the forces acting upon it,
you have 'solved' for its complete history. This world-line does not change
with time, but simply exists as a timeless object. Similarly, in general
relativity, when you solve equations for the shape of space-time, this shape
does not change in time, but exists as a complete timeless object. You can
slice it here and there to examine what the geometry of space looks like at a
particular instant. Examining consecutive slices in time will let you see
whether, for example, the universe is expanding or not.
General about Black hole
A Black
hole is a region of spacetime whose gravitational field is so strong
that nothing which enters it, not even light, can escape. The theory of general relativity predicts
that a sufficiently compact mass will
deform spacetime to form a black hole. Around a black hole there is a
mathematically defined surface called an event horizon that marks the point of no return. It
is called "black" because it absorbs all the light that hits the
horizon, reflecting nothing, just like a perfect black body in thermodynamics. Quantum mechanics predicts that black holes emitradiation like a black body with a finite temperature. This
temperature is inversely proportional to the mass of the black hole, making it
difficult to observe this radiation for black holes of stellar mass or
greater.
Objects whose gravity field is too strong for light to escape were
first considered in the 18th century by John Michell and Pierre-Simon Laplace. The first modern solution of general
relativity that would characterize a black hole was found by Karl Schwarzschild in
1916, although its interpretation as a region of space from which nothing can
escape was not fully appreciated for another four decades. Long considered a
mathematical curiosity, it was during the 1960s that theoretical work showed
black holes were a generic prediction of general relativity. The discovery of neutron stars sparked interest in gravitationally collapsed compact
objects as a possible astrophysical reality.
Black holes of stellar mass are
expected to form when a star of more than 5 solar masses runs out of energy
fuel. This results in the outer layers of gas being thrown out in a supernova
explosion. The core of the star collapses and becomes super dense where even
the atomic nuclei are squeezed together. The energy density at the core goes to
infinity. After a black hole has formed it can continue to grow by absorbing
mass from its surroundings. By absorbing other stars and merging with other black
holes,supermassive black holes of
millions of solar masses may form. There is general consensus that supermassive
black holes exist in the centers of most galaxies. In particular, there is strong
evidence of a black hole of more than 4 million solar masses at the center of our galaxy, the Milky Way.
Despite its invisible interior, the
presence of a black hole can be inferred through its interaction with other matter and
with light and
other electromagnetic radiation. From stellar movement, the mass and
location of an invisible companion object can be calculated. A half-dozen or so
binary star systems have been discovered by astronomers where one of the stars
is invisible, yet must surely exist since it pulls with enough gravitational force
on the other visible star to make it orbit around their common center of
gravity. Therefore these invisible stars are thought to be good candidate black
holes. Astronomers have identified numerous stellar black hole candidates in binary systems by studying the movement of their
companion stars in this way.
History
a galaxy in the background (larger animation).
The idea of a body so massive that even
light could not escape was first put forward by geologist John Michell in a letter written to Henry Cavendish in 1783 of 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.
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 19th
century, since it was not understood how a massless wave such as light could be
influenced by gravity.
General relativity
In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does
influence light's motion. Only a few months later, Karl Schwarzschild found
a solution to Einstein field equations, which describes the gravitational field of
a point mass and a spherical mass. A few months
after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz,
independently gave the same solution for the point mass and wrote more
extensively about its properties. This solution had a peculiar behaviour at
what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein
equations became infinite. The nature of this surface was not quite understood
at the time.
In 1924, Arthur Eddington showed that the singularity
disappeared after a change of coordinates (see Eddington–Finkelstein coordinates), although it
took until 1933 for Georges
Lemaître to realize
that this meant the singularity at the Schwarzschild radius was an unphysical coordinate singularity.
In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity,
that a non-rotating body of electron-degenerate matter above a certain
limiting mass (now called the Chandrasekhar limit at
1.4 solar masses) has no stable solutions. His arguments were opposed by many
of his contemporaries like Eddington and Lev Landau, who
argued that some yet unknown mechanism would stop the collapse. They were
partly correct: a white dwarf slightly more massive than the
Chandrasekhar limit will collapse into aneutron star, which
is itself stable because of the Pauli exclusion principle.
But in 1939, Robert Oppenheimer and
others predicted that neutron stars above approximately three solar masses (the Tolman–Oppenheimer–Volkoff limit) would
collapse into black holes for the reasons presented by Chandrasekhar, and
concluded that no law of physics was likely to intervene and stop at least some
stars from collapsing to black holes.
Oppenheimer and his co-authors
interpreted the singularity at the boundary of the Schwarzschild radius as
indicating that this 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," 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.
Golden age
In 1958, David Finkelstein identified the Schwarzschild surface
as an event horizon,
"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. Finkelstein's solution extended the Schwarzschild solution
for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal, who
was urged to publish it.
These results came at the beginning of
the golden age of general relativity, which was
marked by general relativity and black holes becoming mainstream subjects of
research. This process was helped by the discovery of pulsars in
1967, which, by 1969, were shown to be rapidly rotating neutron stars. Until
that time, neutron stars, like black holes, were regarded as just theoretical
curiosities; but the discovery of pulsars showed their physical relevance and
spurred a further interest in all types of compact objects that might be formed
by gravitational collapse.
In this period more general black hole
solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both
rotating and electrically charged.
Through the work of Werner Israel, Brandon Carter, and
David Robinson the no-hair theorem emerged, stating that a stationary
black hole solution is completely described by the three parameters of the Kerr-Newman metric; mass, angular momentum,
andelectric
charge.
For a long time, it was suspected that
the strange features of the black hole solutions were pathological artifacts
from the symmetry conditions imposed, and that the singularities would not
appear in generic situations. This view was held in particular by Vladimir Belinsky, Isaak Khalatnikov, and Evgeny Lifshitz,
who tried to prove that no singularities appear in generic solutions. However,
in the late sixties Roger Penrose and Stephen Hawking used global techniques to prove that
singularities are generic.
Work by James Bardeen, Jacob Bekenstein,
Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics. These laws describe the behaviour
of a black hole in close analogy to the laws of thermodynamics by
relating mass to energy, area to entropy, and surface gravity to temperature. The
analogy was completed when Hawking, in 1974, showed that quantum field theory predicts
that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole.
The term "black hole" was
first publicly used by John Wheeler during
a lecture in 1967. Although he is usually credited with coining the phrase, he
always insisted that it was suggested to him by somebody else. The first
recorded use of the term is in a 1964 letter by Anne Ewing to the American Association for the
Advancement of Science. After Wheeler's use of the term, it was
quickly adopted in general use.
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 indistinguishable according to classical (i.e.
non-quantum) mechanics.
These properties are special because
they are visible from outside a black hole. For example, a charged black hole
repels other like charges just like any other charged object. Similarly, the
total mass inside a sphere containing a black hole can be found by using the
gravitational analog of Gauss's law, the ADM mass, far away
from the black hole. Likewise, the angular momentum can be measured from far
away using frame dragging by the gravitomagnetic field.
When an object falls into a black hole,
any information about
the shape of the object or distribution of charge on it is evenly distributed along
the horizon of the black hole, and is lost to outside observers. The behavior
of the horizon in this situation is a dissipative system that
is closely analogous to that of a conductive stretchy membrane with friction
and electrical resistance-the membrane paradigm. This
is different from other field theories like
electromagnetism, which do not have any friction or resistivity at the
microscopic level, because they are time-reversible.
Because a 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 a 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.
Physical properties
The simplest black holes have mass but
neither electric charge nor angular momentum. These black holes are often
referred to asSchwarzschild black holes after
Karl Schwarzschild who discovered this solution in
1916. According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.[36] 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 a black hole's horizon; far away, the external gravitational field is
identical to that of any other body of the same mass.
Solutions describing more general black
holes also exist. Charged black holes are
described by the Reissner–Nordström metric, while the Kerr metric describes a rotating black hole. The most general stationary black
hole solution known is the Kerr–Newman metric, which describes a black hole with 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 Planck
units, the total electric charge Q and the total angular momentum J are expected to satisfy: Q2 +(J/M)2
≤ M2 for a black hole of mass M.
Black holes saturating this inequality are called extremal. Solutions of Einstein's equations that violate this
inequality exist, but they do not possess an event horizon. These solutions
have so-called naked singularities that can be observed from the outside,
and hence are deemed unphysical.
The cosmic censorship hypothesis rules out the formation of such
singularities, when they are created through the 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. The black-hole candidate binary X-ray source GRS 1915+105 appears
to have an angular momentum near the maximum allowed value.
Black hole classifications
|
||
Class
|
Mass
|
Size
|
~105–109 MSun
|
~0.001–10 AU
|
|
~103 MSun
|
~103 km
= REarth
|
|
~10 MSun
|
~30 km
|
|
up to ~MMoon
|
up to ~0.1 mm
|
|
Black holes are commonly classified
according to their mass, independent of angular momentum J or electric charge Q. The size of a black hole, as
determined by the radius of the event horizon, or Schwarzschild radius, is roughly proportional to the mass M through:
rsh=[2GM/c2]
~2.95 [M/MSun] km
where rsh is the Schwarzschild radius and MSun is the mass of the Sun. This
relation is exact only for black holes with zero charge and angular momentum;
for more general black holes it can differ up to a factor of 2.
Event horizon
Far away from the black hole a particle can move in any direction, as
illustrated by the set of arrows. 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 through which matter and light can
only pass inward towards the mass of the black hole. Nothing, not even light,
can escape from inside the event horizon. The event horizon is referred to as
such because if an event occurs within the boundary, information from that
event cannot reach an outside observer, making it impossible to determine if
such an event occurred.
As predicted by general relativity, the
presence of a mass deforms spacetime in such a way that the paths taken by
particles bend towards the mass. At the event horizon of a black hole,
this deformation becomes so strong that there are no paths that lead away from the
black hole.
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, an object falling
into a black hole appears to 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 redshift. Eventually,
at a point just before it reaches the event horizon, the falling object becomes
so dim that it can no longer be seen.
On the other hand, an observer falling
into a black hole does not notice any of these effects as he crosses the event
horizon. According to his own clock, he crosses the event horizon after a
finite time, although he is unable to determine exactly when he crosses it, as
it is impossible to determine the location of the event horizon from local
observations.
The shape of the event horizon of a
black hole is always approximately spherical. For
non-rotating (static) black holes the geometry is precisely spherical, while
for rotating black holes the sphere is somewhat oblate.
Singularity
At the center of a black hole as
described by general relativity lies a gravitational singularity, a region where the spacetime
curvature becomes infinite. For a
non-rotating black hole, this region takes the shape of a single point and for
a rotating black hole, it is smeared out to form a ring singularity lying in the plane of rotation. In both cases, the singular region has
zero volume. It can also be shown that the singular region contains all the
mass of the black hole solution. The
singular region can thus be thought of as having infinite density.
Observers falling into a Schwarzschild
black hole (i.e. non-rotating and no charges) cannot avoid being carried into
the singularity, once they cross the event horizon. They can prolong the
experience by accelerating away to slow their descent, but only up to a point;
after attaining a certain ideal velocity, it is best to free fall the rest of the way. When they reach the singularity, they
are crushed to infinite density and their mass is added to the total of the
black hole. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect".
In the case of a charged
(Reissner–Nordström) or rotating (Kerr) black hole, it is possible to avoid the
singularity. Extending these solutions as far as possible reveals the
hypothetical possibility of exiting the black hole into a different spacetime
with the black hole acting as a wormhole. The possibility of traveling to
another universe is however only theoretical, since any perturbation will
destroy this possibility. It also appears to be possible to follow closed timelike curves (going
back to one's own past) around the Kerr singularity, which lead to problems
with causality like
the grandfather paradox. It is expected that none of these
peculiar effects would survive in a proper quantum mechanical treatment of
rotating and charged black holes.
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 aredynamically 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
.png)
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.
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. 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 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, Penrose
proved that a singularity will form somewhere inside it. Shortly afterwards, Hawking showed
that many cosmological solutions describing the Big Bang have singularities without scalar
fields or other exotic matter (seePenrose-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 through stellar nucleosynthesis, or because a star that would have
been stable receives extra matter in a way that 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. The
type of compact star formed depends on the mass of the remnant-the matter left
over after the outer layers have been blown away, such from a supernova explosion or by pulsations leading to
a planetary nebula.
Note that this mass can be substantially less than the original star-remnants
exceeding 5 solar masses are produced by stars that were over 20 solar masses before
the collapse.
If the mass of the remnant exceeds
about 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 ofneutrons is insufficient to stop the collapse.
No known mechanism (except possibly quark degeneracy pressure, see quark star) is
powerful enough to stop the implosion and the object will inevitably collapse
to form a black hole.
The gravitational collapse of heavy
stars is assumed to be responsible for the formation of stellar mass black holes. Star formation in the early universe may have
resulted in very massive stars, which upon their collapse would have produced
black holes of up to 103solar masses. These black holes could be the
seeds of the supermassive black holes found in the centers of most galaxies.
While most of the energy released
during gravitational collapse is emitted very quickly, an outside observer does
not actually see the end of this process. Even though the collapse takes a finite
amount of time from the reference frame of
infalling matter, a distant observer sees the infalling material slow and halt
just above the event horizon, due to gravitational time dilation. Light from the
collapsing material takes longer and longer to reach the observer, with the
light emitted just before the event horizon forms is delayed an infinite amount
of time. Thus the external observer never sees the formation of the event
horizon; instead, the collapsing material seems to become dimmer and
increasingly red-shifted, eventually fading away.
Primordial black holes in the Big Bang
Gravitational collapse requires great
density. 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 that
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
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 be
formed in high-energy collisions
that achieve sufficient density. As of 2002, no such events have 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 (mP = √ħc/G ≈ 1.2×1019 GeV/c2 ≈ 2.2×10−8 kg),
where quantum effects are expected to invalidate the predictions of general
relativity. This would put the creation of black holes firmly out of reach of
any high energy process occurring on or near the Earth. However, certain
developments in quantum gravity suggest that the Planck mass could be much
lower: some braneworld scenarios for example put the boundary
as low as 1 TeV/c2.
This would make it conceivable for micro black holesto
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. Yet these theories are very
speculative, and the creation of black holes in these processes is deemed
unlikely by many specialists. Even if micro black holes should be formed in
these collisions, it is expected that they would evaporate in
about 10−25 seconds,
posing no threat to the Earth.
Growth
Once a black hole has formed, it can
continue to grow by absorbing additional matter. Any black hole will
continually absorb gas andinterstellar dust from its direct surroundings and
omnipresent cosmic background radiation. This is the
primary process through which supermassive black holes seem to have grown. A
similar process has been suggested for the formation of intermediate-mass black holes in globular clusters.
Another possibility is for a black hole
to merge with other objects such as stars or even other black holes. This is
thought to have been important especially for the early development of
supermassive black holes, which could have formed from the coagulation of many
smaller objects. The process has also been proposed as the origin of some intermediate-mass black holes.
Evaporation
In 1974, Hawking showed that black
holes are not entirely black but emit small amounts of thermal radiation; an
effect that has become known as Hawking radiation.
By applying quantum field theory to
a static black hole background, he determined that a black hole should emit
particles in a perfect black body spectrum. Since Hawking's publication, many others
have verified the result through various approaches. If Hawking's theory of black hole
radiation is correct, then black holes are expected to shrink and evaporate over
time because they lose mass by the emission of photons and other particles. The temperature of this thermal
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. Hence, large
black holes emit less radiation than small black holes.
A stellar black hole of one solar mass
has a Hawking temperature of about 100 nanokelvins. This
is far less than the 2.7 K temperature of the cosmic microwave background radiation. Stellar mass or larger
black holes receive more mass from the cosmic microwave background than they
emit through Hawking radiation and thus will grow instead of shrink. To have a
Hawking temperature larger than 2.7 K (and be able to evaporate), a black
hole needs to have less mass than the Moon. Such a black hole would have a
diameter of less than a tenth of a millimeter.
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 would have a diameter of about 10−24 m and take
a nanosecond to evaporate, during which time it would briefly have a luminosity
more than 200 times that of the sun. Lower mass 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. 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
two black holes that
ingest gas from companion stars.
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 hole 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. NASA's Fermi Gamma-ray Space Telescopelaunched in 2008
will continue the search for these flashes.
Astrophysicists
searching for black holes thus have to rely on indirect observations. A black
hole's existence can sometimes be inferred by observing its gravitational
interactions with its surroundings. A project run by MIT's Haystack Observatory is
attempting to observe the event horizon of a black hole directly. Initial
results are encouraging.
The Black hole at the core of Milky Way galaxy
Accretion of matter
Due to conservation of angular momentum, gas falling
into the gravitational well created
by a massive object will typically form a disc-like structure around the
object. Friction within the disc causes angular momentum to be transported
outward, allowing matter to fall further inward, releasing potential energy and
increasing the temperature of the gas.[92] In the case of compact objects such as white dwarfs, neutron stars, and
black holes, the gas in the inner regions becomes so hot that it will emit vast
amounts of radiation (mainly X-rays), which may be detected by telescopes. This
process of accretion is one of the most efficient energy-producing processes
known; up to 40% of the rest mass of the accreted material can be emitted in
radiation.[92] (In nuclear fusion only about 0.7% of
the rest mass will be emitted as energy.) In many cases, accretion discs are
accompanied by relativistic jets emitted
along the poles, which carry away much of the energy. The mechanism for the
creation of these jets is currently not well understood.
As such many of the universe's more
energetic phenomena have been attributed to the accretion of matter on black
holes. In particular, active galactic nuclei and quasars are
believed to be the accretion discs of supermassive black holes. Similarly,
X-ray binaries are generally accepted to be binary starsystems
in which one of the two stars is a compact object accreting matter from its
companion. It has also been
suggested that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.
X-ray binaries
X-ray binaries are binary star systems that are luminous in the X-ray part
of the spectrum. These X-ray emissions are generally thought to be caused by
one of the component stars being a compact object accreting matter from the
other (regular) star. The presence of an ordinary star in such a system
provides a unique opportunity for studying the central object and determining
if it might be a black hole.
Artist impression of a binary system
with an accretion disk around
a black hole being fed by material from the
companion star.
If such a system emits signals that can
be directly traced back to the compact object, it cannot be a black hole. The
absence of such a signal does, however, not exclude the possibility that the
compact object is a neutron star. By studying the companion star it is often
possible to obtain the orbital parameters of the system and obtain an estimate
for the mass of the compact object. If this is much larger than the
Tolman–Oppenheimer–Volkoff limit (that is, the maximum mass a neutron star can
have before collapsing) then the object cannot be a neutron star and is
generally expected to be a black hole.
The
first strong candidate for a black hole, Cygnus X-1, was
discovered in this way by Charles Thomas Bolton, Louise
Webster and Paul Murdin in 1972. Some doubt, however, remained due
to the uncertainties resultant from the companion star being much heavier than
the candidate black hole. Currently, better candidates for black holes are
found in a class of X-ray binaries called soft X-ray transients. In this class of system the companion
star is relatively low mass allowing for more accurate estimates in the black
hole mass. Moreover, these systems are only active in X-ray for several months
once every 10-50 years. During the period of low X-ray emission (called
quiescence), the accretion disc is extremely faint allowing for detailed
observation of the companion star during this period. One of the best such
candidates is V404 Cyg.
Quiescence and advection-dominated accretion flow
The faintness of the accretion disc
during quiescence is suspected 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 as the highly energetic gas hits the surface, an effect that is observed
for neutron stars in a similar state.
Quasi-periodic oscillations
The X-ray emission from accretion disks
sometimes flickers at certain frequencies. These signals are called quasi-periodic oscillations and are thought to be caused by
material moving along the inner edge of the accretion disk (the innermost
stable circular orbit). As such their frequency is linked to the mass of the
compact object. They can thus be used as an alternative way to determine the
mass of potential black holes.
Galactic nuclei
Astronomers use the term "active galaxy"
to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio
emission. Theoretical and observational studies have shown that the activity in
these active galactic nuclei (AGN) may be explained by the presence of
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.
It is now widely accepted that the
center of (nearly) every galaxy (not just active ones) 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.
Currently, the best evidence for a
supermassive black hole comes from studying the proper motion of stars near the center of our own Milky Way. Since
1995 astronomers have tracked the motion of 90 stars in a region called Sagittarius A*. By
fitting their motion to Keplerian orbits they were able to infer in 1998 that
2.6 million solar masses must be contained in a volume with a
radius of 0.02 lightyears. Since
then one of the stars-called S2-has completed a
full orbit. From the orbital data they were able to place better constraints on
the mass and size of the object causing the orbital motion of stars in the
Sagittarius A* region, finding that there is a spherical mass of 4.3 million
solar masses contained within a radius of less than 0.002 lightyears. While
this is more than 3000 times the Schwarzschild radius corresponding to that
mass, it is at least consistent with the central object being a supermassive
black hole, and no "realistic cluster [of stars] is physically
tenable."
Gravitational lensing
The deformation of spacetime around a
massive object causes light rays to be deflected much like light passing through
an opticlens.
This phenomenon is known as gravitational lensing. Observations have been made of weak
gravitational lensing, in which photons are deflected by only a few arcseconds.
However, it has never been directly observed for a black hole. One possibility for observing
gravitational lensing by a black hole would be to observe stars in orbit around
the black hole. There are several candidates for such an observation in orbit
around Sagittarius A*.
Alternatives
The evidence for stellar black holes
strongly relies on the existence of an upper limit for the mass of a neutron
star. The size of this limit heavily depends on the assumptions made about the
properties of dense matter. New exotic phases of matter could push up this bound. A phase of free quarks at
high density might allow the existence of dense quark stars, and some supersymmetricmodels
predict the existence of Q stars. Some
extensions of the standard model posit the existence of preons as
fundamental building blocks of quarks and leptons, which could hypothetically form preon stars. These
hypothetical models could potentially explain a number of observations of
stellar black hole candidates. However, it can be shown from general arguments
in general relativity that any such object will have a maximum mass.
Since
the average density of a black hole inside its Schwarzschild radius is inversely
proportional to the square of its mass, supermassive black holes are much less
dense than stellar black holes (the average density of a 108 solar mass black hole is comparable to
that of water). Consequently, the physics of matter
forming a supermassive black hole is much better understood and the possible
alternative explanations for supermassive black hole observations are much more
mundane. For example, a supermassive black hole could be modelled by a large
cluster of very dark objects. However, typically such alternatives are not
stable enough to explain the supermassive black hole candidates.
The evidence for stellar and
supermassive black holes implies that in order for black holes not to form,
general relativity must fail as a theory of gravity, perhaps due to the onset
of quantum mechanical corrections. A much anticipated feature
of a theory of quantum gravity is that it will not feature singularities or
event horizons (and thus no black holes). In recent years, much attention has
been drawn by the fuzzball model
in string theory.
Based on calculations in specific situations in string theory, the proposal
suggest that generically the individual states of a black hole solution do not
have an event horizon or singularity, but that for a classical/semi-classical
observer the statistical average of such states does appear just like an
ordinary black hole in general relativity.
Open questions
Entropy and thermodynamics
In 1971, Hawking showed under general
conditions that the total area of the event horizons of any
collection of classical black holes can never decrease, even if they collide
and merge. This result, now known as the second law of black hole mechanics, is
remarkably similar to the second law of thermodynamics, which states that
the totalentropy of a system can never decrease. As
with classical objects at absolute zerotemperature,
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
a black hole, resulting in a decrease of the total entropy of the universe.
Therefore, Bekenstein proposed that a black hole should have an entropy, and
that it should be proportional to its horizon area.
The
link with the laws of thermodynamics was further strengthened by Hawking's
discovery that quantum field theory predicts
that a black hole radiates blackbody radiation at
a constant temperature. This seemingly causes a violation of the second law of
black hole mechanics, since the radiation will carry away energy from the black
hole causing it to shrink. The radiation, however also carries away entropy,
and it can be proven under general assumptions that the sum of the entropy of
the matter surrounding a black hole and one quarter of the area of the horizon
as measured in Planck units is in fact always increasing. This
allows the formulation of the first law of black hole mechanics as an analogue of the first law of thermodynamics, with the mass
acting as energy, the surface gravity as temperature and the area as entropy.
One
puzzling feature is that the entropy of a black hole scales with its area
rather than with its volume, since entropy is normally anextensive quantity that
scales linearly with the volume of the system. This odd property led Gerard 't Hooft and Leonard Susskind to propose the holographic principle, which suggests that anything that
happens in a volume of spacetime can be described by data on the boundary of
that volume.
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 that have the same macroscopic
qualities (such as mass, charge, pressure, etc.).
Without a satisfactory theory of quantum gravity,
one cannot perform such a computation for black holes. Some progress has been
made in various approaches to quantum gravity. In 1995, Andrew Strominger and Cumrun Vafa showed that counting the microstates
of a specific supersymmetric black hole in string theory reproduced the Bekenstein-Hawking
entropy.[118] Since then, similar results have been
reported for different black holes both in string theory and in other
approaches to quantum gravity like loop quantum gravity.
Black hole unitarity
An open question in fundamental physics
is the so-called information loss paradox, orblack 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 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).
References
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