Black Holes

A black hole is a region of space in which the gravitational field is so powerful that nothing, not even light, can escape its pull after having fallen past its event horizon. The name comes from the fact that, at a certain point, even electromagnetic radiation (e.g. visible light) is unable to break away from the attraction of these massive objects. This renders the hole's interior invisible or, rather, black like the appearance of space itself.

Despite its interior being invisible a black hole hole may betray its presence through in interaction with matter that lies in orbit outside its event horizon. For example, a black hole may be perceived by tracking the movement of a group of stars that orbit its center. Alternatively, one may observe the product of gas (from a nearby star, for instance) that has been drawn into the black hole. The 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.[2][3][4] Such observations have resulted in the general scientific consensus that — barring a breakdown of our understanding nature— black holes do exist in our universe.[5]

While the idea of an object with gravity strong enough to prevent light from escaping was proposed in the 18th century,[6] black holes, as currently understood, are described by Einstein's general theory of relativity, which he developed in 1916. This theory predicts that when a large enough amount of mass is present in a sufficiently small region of space, all paths through space are warped inwards towards the center of the volume, preventing all matter and radiation within it from escaping.

While general relativity describes a black hole as a region of empty space with a pointlike singularity at the center and an event horizon at the outer edge, the description changes when the effects of quantum mechanics are taken into account. Research on this subject indicates that, rather than holding captured matter forever, black holes may slowly leak a form of thermal energy called Hawking radiation.[7][8][9] However, the final, correct description of black holes, requiring a theory of quantum gravity, is unknown.

Contents

What makes it impossible to escape from black holes?

Popular accounts commonly try to explain the black hole phenomenon by using the concept of escape velocity, the speed needed for an vessel starting at the surface of a massive object to completely clear the object's gravitational field. Using Newton's law of gravity it is straight forward to show that if you take a sufficiently dense object its escape velocity will equal or even exceed the speed of light. Citing that nothing can exceed the speed of light they then infer that nothing would be able escape such a dense object. Of course, this argument has a flaw in that it doesn't explain why light would even be effected by a gravitating body, let along why it wouldn't be able to escape. Sometimes some arguments are added arguing that in general relativity light is affected by gravity and that indeed the energy required to escape a black hole is infinite. This makes the argument slightly better, but still this really does not explain what is going on.

To really understand what is going on we need two lessons taught to us by Albert Einstein. The first is that time and space are not two independent concepts, but are interrelated forming a single continuum, spacetime. This continuum has some special properties. An object is not free to move around spacetime at will, instead it must always move forwards in time. In fact, not only must an object move forwards in time, it also cannot change its position faster than the speed of light. This is the main result of the theory of special relativity.

The second lesson we need is the main message of general relativity, mass deforms the structure of spacetime. Loosely speaking the effect of a mass on spacetime is too slightly tilt the direction of time towards the mass. As a result objects tend to move towards masses, we experience this as gravity. As you get closer to a mass this tilting effect becomes stronger. At some point close to the mass this effect becomes so strong that all the possible paths an object can take lead towards the mass. That is, you can no longer get further away from the black hole no matter how much you try; you are trapped. This is precisely what happens at the event horizon of a black hole.

So, to put it succinctly, the reason you cannot escape a black hole is because you cannot move backwards in time (or faster than the speed of light).

Sizes of black holes

Black holes can have any mass. Since the gravitational force of a body on itself, at the surface of a body of any shape, increases in inverse proportion to its characteristic lengthscale squared (as volume-2/3 ), an object of any shape and mass that is sufficiently compressed will collapse under its own gravity and form a black hole. However, when black holes form naturally, only a few mass ranges are realistic.

Black holes can be divided into several size categories:


 

Black hole parameters and the "no hair theorem"

Main article: No hair theorem

The "No hair" theorem states that black holes have only 3 independent internal properties: mass, angular momentum and electric charge. As a consequence it is impossible to tell the difference between a black hole formed from a highly compressed mass of normal matter and one formed from, say, a highly compressed mass of anti-matter; in other words, any other information (apart from mass, angular momentum and charge) about infalling matter or energy is seemingly destroyed. This is the black hole information paradox.

The theorem only works in some of the types of universe that the equations of general relativity allow, but this includes four-dimensional spacetimes with a zero or positive cosmological constant, which describes our universe at the classical level.

Types of black holes

Despite the uncertainty about whether the "No Hair" theorem applies to our universe, astrophysicists currently classify black holes according to their angular momentum (non-zero angular momentum means the black hole is rotating) and electric charge:

  Non-rotating Rotating
Uncharged Schwarzschild Kerr
Charged Reissner-Nordström Kerr-Newman

(All black holes have non-zero mass, so mass cannot be used for this type of "yes" / "no" classification)

Physicists do not expect that black holes with a significant electric charge will be formed in nature, because the electromagnetic repulsion that resists the compression of an electrically charged mass is about 40 orders of magnitude greater (about 1040 times greater) than the gravitational attraction that compresses the mass. So this article does not cover charged black holes in detail, but the Reissner-Nordström black hole and Kerr-Newman metric articles provide more information.

On the other hand astrophysicists expect that almost all black holes will rotate because the stars from which they are formed rotate. In fact most black holes are expected to spin very rapidly, because they retain most of the angular momentum of the stars from which they were formed, but concentrated into a much smaller radius. The same laws of angular momentum make skaters spin faster if they pull their arms closer to their bodies.

This article describes non-rotating, uncharged black holes first, because they are the simplest type.

Major features of non-rotating, uncharged black holes

Event horizon

This is the boundary of the region from which not even light can escape, but at the same time, light does not get sucked into the black hole. Stephen Hawking, in his book A Brief History of Time, describes the event horizon as "the point of which light is just barely able to escape ("I like to think of it as being chased by the police but just barely managing to stay one step away!")." Another way to think of this is that the light is running on a spacetime "treadmill;" the light is moving away from the black hole at the rate of c, but the spacetime is being sucked into the black hole at the same rate, so the two cancel each other out, much like a treadmill. An observer at a safe distance would see a dull black disc if the black hole was in a pure vacuum but in front of a light background, such as a bright nebula. The event horizon is not a solid surface, and does not obstruct or slow down matter or radiation that is traveling towards the region within the event horizon.

The event horizon is the defining feature of a black hole—it is black because no light or other radiation can escape from inside it, excluding Hawking radiation. So the event horizon hides whatever happens inside it, and we can only calculate what happens by using the best theory available, which at present is general relativity.

The gravitational field outside the event horizon is identical to the field produced by any other spherically symmetric object of the same mass. The popular conception of black holes as "sucking" things in is false: objects can maintain an orbit around black holes indefinitely, provided they stay outside the photon sphere (described below), and also ignoring the effects of gravitational radiation, which causes orbiting objects to lose energy, similar to the effect of electromagnetic radiation.

Singularity at a single point

According to general relativity, a black hole's mass is entirely compressed into a region with zero volume, which means its density and gravitational pull are infinite, and so is the curvature of space-time that it causes. These infinite values cause most physical equations, including those of general relativity, to stop working at the center of a black hole. So physicists call the zero-volume, infinitely dense region at the center of a black hole a singularity.

The singularity in a non-rotating, uncharged black hole is a point, in other words it has zero length, width, and height.

But there is an important uncertainty about this description: quantum mechanics is as well-supported by mathematics and experimental evidence as general relativity, and it does not allow objects to have zero size—so quantum mechanics says the center of a black hole is not a singularity but just a very large mass compressed into the smallest possible volume. At present we have no well-established theory that combines quantum mechanics and general relativity; and the most promising candidate, string theory, also does not allow objects to have zero size.

The rest of this article will follow the predictions of general relativity, because quantum mechanics deals with very small-scale (sub-atomic) phenomena and general relativity is the best theory we have at present for explaining large-scale phenomena, such as the behavior of masses similar to or larger than stars.

Photon sphere

A non-rotating black hole's 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 that of the event horizon. This may give the impression that a black hole will accumulate a 'shell' of captured photons, which will grow in density indefinitely, but this is not true. No photon is likely to stay in this orbit for long, for two reasons. First, it is likely to interact with any infalling matter in the vicinity (being absorbed or scattered). Second, the orbit is dynamically unstable due to light's enormous speed; small deviations from a perfectly circular path will grow into larger deviations very quickly, causing the photon to either escape or fall into the hole.

Other extremely compact objects, such as neutron stars, can also have photon spheres.[10] This follows from the fact that light "captured" by a photon sphere does not pass within the radius that would form the event horizon if the object were a black hole of the same mass, and therefore its behavior does not depend on the presence of an event horizon.


 

Major features of rotating black holes

Main article: Rotating black hole
Two important surfaces around a rotating black hole. The inner sphere is the static limit (the event horizon). It is the inner boundary of a region called the ergosphere. The oval-shaped surface, touching the event horizon at the poles, is the outer boundary of the ergosphere. Within the ergosphere a particle is forced (dragging of space and time) to rotate and may gain energy at the cost of the rotational energy of the black hole (Penrose process).
Two important surfaces around a rotating black hole. The inner sphere is the static limit (the event horizon). It is the inner boundary of a region called the ergosphere. The oval-shaped surface, touching the event horizon at the poles, is the outer boundary of the ergosphere. Within the ergosphere a particle is forced (dragging of space and time) to rotate and may gain energy at the cost of the rotational energy of the black hole (Penrose process).

Rotating black holes share many of the features of non-rotating black holes—the inability of light or anything else to escape from within their event horizons, accretion disks, etc. But general relativity predicts that rapid rotation of a large mass produces further distortions of space-time, in addition to those that a non-rotating large mass produces; and these additional effects make rotating black holes strikingly different from non-rotating ones.

Ergosphere

A large, ultra-dense rotating mass creates an effect called frame-dragging, so that space-time is dragged around it in the direction of the rotation.

Rotating black holes have an ergosphere, a region bounded by

  • on the outside, an oblate spheroid, which coincides with the event horizon at the poles and is noticeably wider around the "equator". This boundary is sometimes called the "ergosurface", but it is just a boundary and has no more solidity than the event horizon. At points exactly on the ergosurface, space-time is dragged around at the speed of light.
  • on the inside, the outer event horizon.

Within the ergosphere, space-time is dragged around faster than light—general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.

Objects and radiation (including light) can stay in orbit within the ergosphere without falling to the center. But they cannot hover (remain stationary, as seen by an external observer), because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.

Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way, the black hole will spin more slowly and may even stop spinning eventually.

Ring-shaped singularity

General relativity predicts that a rotating black hole will have a ring singularity which lies in the plane of the "equator" and has zero width and thickness—but remember that quantum mechanics does not allow objects to have zero size in any dimension (their wavefunction must spread), so general relativity's prediction is only the best idea we have until someone devises a theory that combines general relativity and quantum mechanics.

Possibility of escaping from a rotating black hole

Penrose diagrams of various Schwarzschild solutions. Time is the vertical dimension, space is horizontal, and light travels at 45° angles. Paths less than 45° to the horizontal are forbidden by special relativity, but rotating black holes allow for travel to future "universes"
Penrose diagrams of various Schwarzschild solutions. Time is the vertical dimension, space is horizontal, and light travels at 45° angles. Paths less than 45° to the horizontal are forbidden by special relativity, but rotating black holes allow for travel to future "universes"

Kerr's solution for the equations of general relativity predicts that:

  • The properties of space-time between the two event horizons allow objects to move only towards the singularity.
  • But the properties of space-time within the inner event horizon allow objects to move away from the singularity, pass through another set of inner and outer event horizons, and emerge out of the black hole into another universe or another part of this universe without traveling faster than the speed of light.
  • Passing through the ring shaped singularity may allow entry to a negative gravity universe.[11]

If this is true, rotating black holes could theoretically provide the wormholes which often appear in science fiction. Unfortunately, it is unlikely that the internal properties of a rotating black hole are exactly as described by Kerr's solution[12] and it is not currently known whether the actual properties of a rotating black hole would provide a similar escape route for an object via the inner event horizon.

Even if this escape route is possible, it is unlikely to be useful because a spacecraft which followed that path would probably be distorted beyond recognition by spaghettification.

What happens when something falls into a black hole?

This section describes what happens when something falls into a non-rotating, uncharged black hole. The effects of rotating and charged black holes are more complicated but the final result is much the same—the falling object is absorbed (unless rotating black holes really can act as wormholes).

Spaghettification

Main article: spaghettification

An object in any very strong gravitational field feels a tidal force stretching it in the direction of the object generating the gravitational field. This is because the inverse square law causes nearer parts of the stretched object to feel a stronger attraction than farther parts. Near black holes, the tidal force is expected to be strong enough to deform any object falling into it, even atoms or composite nucleons; this is called spaghettification. The process of spaghettification is as follows. First, the object that is falling into the black hole splits in half. Then the two halves each split in half themselves. Then the four quarters each split in half. This process of bifurcation continues up to and past the point in which the split-up pieces of the original object are at the order of magnitude of atoms. At the end of the spaghettification process, the object is a string of elementary particles.

The strength of the tidal force of a black hole depends on how gravitational attraction changes with distance, rather than on the absolute force being felt. This means that small black holes cause spaghettification while infalling objects are still outside their event horizons, whereas objects falling into large, supermassive black holes may not be deformed or otherwise feel excessively large forces before passing the event horizon.

Before the falling object crosses the event horizon

An object in a gravitational field experiences a slowing down of time, called gravitational time dilation, relative to observers outside the field. The outside observer will see that physical processes in the object, including clocks, appear to run slowly. As a test object approaches the event horizon, its gravitational time dilation (as measured by an observer far from the hole) would approach infinity.

From the viewpoint of a distant observer, an object falling into a black hole appears to slow down, approaching but never quite reaching the event horizon: and it appears to become redder and dimmer, because of the extreme gravitational red shift caused by the gravity of the black hole. Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon. All of this is a consequence of time dilation: the object's movement is one of the processes that appear to run slower and slower, and the time dilation effect is more significant than the acceleration due to gravity; the frequency of light from the object appears to decrease, making it look redder, because the light appears to complete fewer cycles per "tick" of the observer's clock; lower-frequency light has less energy and therefore appears dimmer, as well as redder.

From the viewpoint of the falling object, distant objects generally appear blue-shifted due the gravitational field of the black hole. This effect may be partly (or even entirely) negated by the red shift caused by the velocity of the infalling object with respect to the object in the distance.

As the object passes through the event horizon

From the viewpoint of the falling object, nothing particularly special happens at the event horizon. In fact, the Earth could be passing through an event horizon at just this moment without us ever noticing. An infalling object takes a finite proper time (i.e. measured by its own clock) to fall past the event horizon. This in contrast with the infinite amount of time it takes for a distant observer to see the infalling object cross the horizon.

Inside the event horizon

The object reaches the singularity at the center within a finite amount of proper time, as measured by the falling object. An observer on the falling object would continue to see objects outside the event horizon, blue-shifted or red-shifted depending on the falling object's trajectory. Objects closer to the singularity aren't seen, as all paths light could take from objects farther in point inwards towards the singularity.

The amount of proper time a faller experiences below the event horizon depends upon where they started from rest, with the maximum being for someone who starts from rest at the event horizon. A paper in 2007 examined the effect of firing a rocket pack with the black hole, showing that this can only reduce the proper time of a person who starts from rest at the event horizon. However, for anyone else, a judicious burst of the rocket can extend the lifetime of the faller, but overdoing it will again reduce the proper time experienced. However, this cannot prevent the inevitable collision with the central singularity.[13]

Hitting the singularity

As an infalling object approaches the singularity, tidal forces acting on it approach infinity. All components of the object, including atoms and subatomic particles, are torn away from each other before striking the singularity. At the singularity itself, effects are unknown; it is believed that a theory of quantum gravity is needed to accurately describe events near it. Regardless, as soon as an object passes within the hole's event horizon, it is lost to the outside universe. An observer far from the hole simply sees the hole's mass, charge, and angular momentum change slightly, to reflect the addition of the infalling object's matter. After the event horizon all is unknown. Anything that passes this point cannot be retrieved to study.


 

Formation and evaporation

Formation of stellar-mass black holes

Stellar-mass black holes are formed in two ways:

  • As a direct result of the gravitational collapse of a star.
  • By collisions between neutron stars.[14] Although neutron stars are fairly common, collisions appear to be very rare. Neutron stars are also formed by gravitational collapse, which is therefore ultimately responsible for all stellar-mass black holes.

Stars undergo gravitational collapse when they can no longer resist the pressure of their own gravity. 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 transforms the matter in the star's core into a denser state which forms one of the 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.

Only the largest remnants, those exceeding a particular limit (the Tolman-Oppenheimer-Volkoff limit, not to be confused with the Chandrasekhar limit), generate enough pressure to produce black holes, because black holes are the most radically transformed state of matter known to physics, and the force which resists this level of compression, neutron degeneracy pressure, is extremely strong. But any remnant larger than the Tolman-Oppenheimer-Volkoff limit will never be able to stop collapsing, and when its outer radius falls below its Schwarzschild radius, the transition to black hole is complete.

The collapse process for stars producing remnants this size releases energy which usually produces a supernova, blowing the star's outer layers into space so that they form a spectacular nebula (this sort of nebula is called a supernova remnant). But the supernova is a side-effect and does not directly contribute to producing the black hole (or other type of compact star). For example a few gamma ray bursts were expected to be followed by evidence of supernovae but this evidence did not appear.[15][16] One possible explanation is that some very large stars can form black holes fast enough to swallow the supernova blast wave before it can reach the surface of the star.

Formation of larger black holes

There are two main ways in which black holes of larger than stellar mass can be formed:

  • Stellar-mass black holes may act as "seeds" which grow by absorbing mass from interstellar gas and dust, stars and planets or smaller black holes.
  • Star clusters of large total mass may be merged into single bodies by their members' gravitational attraction. This will usually produce a supergiant or hypergiant star which runs short of "fuel" in a few million years and then undergoes gravitational collapse, produces a supernova or hypernova and spends the rest of its existence as a black hole.

Formation of smaller black holes

No known process currently active in the universe can form black holes of less than stellar mass. This is because all present known black hole formation is through gravitational collapse, and the smallest mass which can collapse to form a black hole produces a hole approximately 1.5-3.0 times the mass of the sun (the Tolman-Oppenheimer-Volkoff limit). Smaller masses collapse to form white dwarf stars or neutron stars.

There are still a few ways in which smaller black holes might be formed, or might have formed in the past.

Evaporation of larger black holes

Larger black holes evaporate. If the initial mass of the hole was stellar mass, the time required for it to lose most of its mass via Hawking evaporation is much longer than the age of the universe, so small black holes are not expected to have formed by this method yet.

Big Bang

The Big Bang produced sufficient pressure to form smaller black holes without the need for anything resembling a star. None of these hypothesized primordial black holes have been detected.

Particle accelerators

In principle, a sufficiently energetic collision within a very powerful particle accelerator could produce a micro black hole. In practice, this is expected to require energies comparable to the Planck energy, which is vastly beyond the capability of any present, planned, or expected future particle accelerator to produce. Some speculative models allow the formation of black holes at much lower energies. This would allow production of extremely short-lived black holes in terrestrial particle accelerators. No evidence of this type of black hole production has been presented as of 2007.

See Micro black hole escaping from a particle accelerator below.

Evaporation

Hawking radiation is a theoretical process by which black holes can evaporate into nothing. As there is no experimental evidence to corroborate it and there are still some major questions about the theoretical basis of the process, there is still debate about whether Hawking radiation can enable black holes to evaporate.

Quantum mechanics says that even the purest vacuum is not completely empty but is instead a "sea" of energy (known as zero-point energy) which has wave-like Fluctuation (thermodynamics). We cannot observe this "sea" of energy directly because there is no lower energy level with which we can compare it. The Heisenberg uncertainty principle dictates that it is impossible to know the exact value of the mass-energy and position pairings. The fluctuations in this sea produce pairs of particles in which one is made of normal matter and the other is the corresponding antiparticle (special relativity proves mass-energy equivalence, i.e. that mass can be converted into energy and vice versa). Normally each would soon meet another instance of its antiparticle and the two would be totally converted into energy, restoring the overall matter-energy balance as it was before the pair of particles was created. The Hawking radiation theory suggests that, if such a pair of particles is created just outside the event horizon of a black hole, one of the two particles may fall into the black hole while the other escapes, because the two particles move in slightly different directions after their creation. From the point of view of an outside observer, the black hole has just emitted a particle and therefore the black hole has lost a minute amount of its mass.

If the Hawking radiation theory is correct, only the very smallest black holes are likely to evaporate in this way. For example a black hole with the mass of our Moon would gain as much energy (and therefore mass - mass-energy equivalence again) from cosmic microwave background radiation as it emits by Hawking radiation, and larger black holes will gain more energy (and mass) than they emit. To put this in perspective, the smallest black hole which can be created naturally at present is about 5 times the mass of our sun, so most black holes have much greater mass than our Moon.

Over time the cosmic microwave background radiation becomes weaker. Eventually it will be weak enough so that more Hawking radiation will be emitted than the energy of the background radiation being absorbed by the black hole. Through this process, even the largest black holes will eventually evaporate. However, this process may take nearly a googol years to complete.

Techniques for finding black holes

Accretion disks and gas jets

Formation of extragalactic jets from a black hole's accretion disk
Formation of extragalactic jets from a black hole's accretion disk

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

A "Quasar" Black Hole.
A "Quasar" Black Hole.

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 round 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[17] or by collisions between neutron stars,[14] 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,[18] 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[19] so the black holes associated with them are actually billions of years old.

Some astrophysicists believe that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.[20]

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.[21]

Gravitational lensing

Gravitational lensing distorts the image around a black hole in front of the Large Magellanic Cloud (simulated view)
Gravitational lensing distorts the image around a black hole in front of the Large Magellanic Cloud (simulated view)

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 Albert Einstein's 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.

Objects orbiting possible black holes

See also: Kepler problem in general relativity

Some large celestial objects are almost certainly orbiting around black holes, and the principles behind this conclusion are surprisingly simple if we consider a circular orbit first (although all known closed astronomical orbits are elliptical):

  • The radius of the central object round which the observed object is orbiting must be less than the radius of the orbit, otherwise the two objects would collide.
  • The orbital period and the radius of the orbit make it easy to calculate the centrifugal force created by the orbiting object. Strictly speaking, the centrifugal force also depends on the orbiting object's mass, but the next two steps show why we can get away with pretending this is a fixed number: e.g., 1.
  • The gravitational attraction between the central object and the orbiting object must be exactly equal to the centrifugal force, otherwise the orbiting body would either spiral into the central object or drift away.
  • The required gravitational attraction depends on the mass of the central object, the mass of the orbiting object, and the radius of the orbit. But we can simplify the calculation of both the centrifugal force and the gravitational attraction by pretending that the mass of the orbiting object is the same fixed number: e.g., 1. This makes it very easy to calculate the mass of the central object.
  • If the Schwarzschild radius for a body with the mass of the central object is greater than the maximum radius of the central object, the central object must be a black hole whose event horizon's radius is equal to the Schwarzschild radius.

Unfortunately, since the time of Johannes Kepler, astronomers have had to deal with the complications of real astronomy:

  • Astronomical orbits are elliptical. This complicates the calculation of the centrifugal force, the gravitational attraction, and the maximum radius of the central body. But Kepler could handle this without needing a computer.
  • The orbital periods in this type of situation are several years, so several years' worth of observations are needed to determine the actual orbit accurately. The "possibly a black hole" indicators (accretion disks, gas jets, radiation emissions, etc.) help "black hole hunters" to decide which orbits are worth observing for such long periods.
  • If there are other large bodies within a few light years, their gravity fields will perturb the orbit. Adjusting the calculations to filter out the effects of perturbation can be difficult, but astronomers are used to doing it.

Determining the mass of Black Holes

Quasi-periodic oscillations can be used to determine the mass of Black Holes.[22] 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 black holes at the centers of galaxies

The jet originating from the center of M87 in this image comes from an active galactic nucleus that may contain a supermassive black hole. Credit: Hubble Space Telescope/NASA/ESA.
The jet originating from the center of M87 in this image comes from an active galactic nucleus that may contain a supermassive black ho