Black
Holes

(Section Not Complete)

Photons always travel at the speed of light, but they lose energy when travelling out of a gravitational field and appear to be redder to an external observer. The stronger the gravitational field, the more energy the photons lose because of this gravitational redshift. The extreme case is a black hole where photons from within a certain radius lose all their energy and become invisible. Indeed, light in the vicinity of such strong gravitational fields exhibits quite bizarre behavior. Here are links to some movies illustrating virtual trips to black holes and neutron stars.

Event Horizons

The event horizon is the point outside the black hole where the gravitational attraction becomes so strong that the escape velocity (the velocity at which an object would have to go to escape the gravitational field) equals the speed of light. Since according to the relativity theory no object can exceed the speed of light, that means that nothing, not even light, could escape the black hole once it is inside this distance from the center of the black hole. A more fundamental way of viewing this is that in a black hole the gravitational field is so intense that it bends space and time around itself so that inside the event horizon there are literally no paths in space and time that lead to the outside of the black hole: No matter what direction you went, you would find that your path led back to the center of the black hole, where the singularity is found.

Black Holes and the Speed of Light

Black holes almost certainly exist, and one of their basic properties is that they trap light. However, it is also true that nothing exceeds the speed of light. In fact, the theoretical prediction of black holes is due to the General Theory of Relativity, which is built on the principle that the speed of light in a vacuum is constant. The analogy of a cannonball falling back to Earth with the trapping of light in a black hole is only a crude and suggestive one that is not correct at a fundamental level (for one thing, the cannonball has mass, but light does not; it turns out that this difference is critical, because massless particles MUST travel at light velocity, but massive particles CANNOT travel at light velocity).

To understand fully why a black hole can trap light but the light still always travels at constant velocity requires an understanding of the General Theory of Relativity, but the essential point is that the black hole curves spacetime back on itself, so that all paths in the interior of the black hole lead back to the singularity at the center, no matter which direction you go (an analogy in two dimensions is that no matter which direction you go on the surface of the Earth in a "straight line" (what mathematicians call a "geodesic" or a "great circle"), you never escape the Earth but instead return to the same point. Imagine extending that analogy to the 4 dimensions of spacetime and you have a rough explanation for why light travels at light speed, but cannot escape the interior of a black hole.

Singularities Clothed and Naked

The singularity is the point of infinite density thought to exist at the center of a black hole. We have no way of understanding what would happen in the vicinity of a singularity, since in essence nature divides our equations by zero at such a point, and you probably learned some time in math class that you cannot divide by zero and get sensible mathematics. There is an hypothesis, called the "Law of Cosmic Censorship" that all singularities in the Universe are contained inside event horizons and therefore are in principle not observable (because no information about the singularity can make it past the event horizon to the outside world). However, this is an hypothesis, not rigorously proven, so it is conceivable that so-called "Naked Singularities" might exist, not clothed by an event horizon. If such were the case, we can only guess at this point what that would imply for physics near such an object.

Violence in the Cosmos Black Holes

Black Holes in Binary Star Systems

It is thought that in some binary systems one of the stars is a black hole. Although the black hole cannot be seen directly, it can signal its presence if matter accretes from the other star into the black hole. The matter falling into the black hole is likely to form an accretion disk.

As the matter in the accretion disk loses energy and spirals downward into the black hole it is heated to very high temperatures and emits X-rays. Generally, any binary star system in which there is a strong X-ray source and in which one of the stars is not seen but is very massive is a good candidate for a black hole.

Identification of Cygnus X-1

Black Hole Accretion

The compact star in an accreting binary system may also be a black hole. Accretion onto a black hole will look similar in many respects to accretion onto a neutron star or white dwarf. The adjacent figure is a ROSAT X-ray image of LMC X-1, a binary system in the Large Magellanic Cloud in which one star is a more normal star and one is estimated to have a mass of 5 solar masses or more and therefore is likely to be a black hole (Source).

The diffuse glow is X-ray emission in the vicinity of the binary (which isn't seen in the image). X-rays from the accretion disk of the binary knock electrons off atoms in a volume of space that may be light years in diameter. These atoms emit X-rays when the electrons re-combine, causing the observed glow. The following table lists candidates black holes in some binary systems.

Black Hole Candidates in Binary Star Systems

Name of
Binary System
Companion Star
Spectral Type
Orbital Period
(days)
Black Hole Mass
(Solar Units)

Cygnus X-1 B supergiant 5.6 6-15
LMC X-3 B main sequence 1.7 4-11
A0620-00 (V616 Mon) K main sequence 7.8 4-9
GS2023+338 (V404 Cyg) K main sequence 6.5 > 6
GS2000+25 (QZ Vul) K main sequence 0.35 5-14
GS1124-683 (Nova Mus 1991) K main sequence 0.43 4-6
GRO J1655-40 (Nova Sco 1994) F main sequence 2.4 4-5
H1705-250 (Nova Oph 1977) K main sequence 0.52 > 4

SOURCE: Fraknoi, Morrison, & Wolff, Voyages through the Universe

Here is a table from a different source:

Stellar Black Holes in the Milky Way
X-Ray Source Name Mass of Companion Mass of Black Hole
Cygnus X-1 24 - 42 11 - 21
V404 Cygni ~ 0.6 10 - 15
GS 2000+25 ~ 0.7 6 - 14
H 1705 - 250 0.3 - 0.6 6.4 - 6.9
GRO J1655 - 40 2.34 7.02
A 0620 - 00 0.2 - 0.7 5 - 10
GS 1124 - T68 0.5 - 0.8 4.2 - 6.5
GRO J042+32 ~ 0.3 6 - 14
4U 1543 - 47 ~ 2.5 2.7 - 7.5
All masses in Solar masses. Source: "Revisiting the Black Hole",
R. Blandford & N. Gehrels, Physics Today, June (1999)

Bipolar Mass Ejection

Some of the material accreting onto a black hole may get ejected at very high velocities along the directions defined by the black hole rotation axis; this is called bipolar flow. The adjacent image shows a Nebula produced by possible bipolar flow from a binary system.

Such mass ejection might also be produced by accretion onto neutron stars. Thus additional information, such as an estimate of the mass of the unseen compact object, is generally required to show that the mass ejection is probably associated with a black hole.

Supermassive Accretion Disks

Accretion into black holes is not limited to binary star systems. The following image shows a composite of ground based optical and radio telescope images of the galaxy NGC 4261, and a high resolution Hubble Space Telescope image of the core of this galaxy.

NGC 4261 has enormous jets shooting from its core and very strong radio frequency emission. It is thought that the jets are powered by a gargantuan black hole of perhaps a billion solar masses, and that the ring in the Hubble image is an accretion disk feeding the black hole.

The black hole itself presumably lies inside the bright spot at the center. Even a billion solar mass black hole would be too small to see in this image.

Black Holes Signature From Advective Disks

Black Holes in Galactic Centers

Virtual trips to black holes & neutron stars

Black hole FAQ

Special Relativity

General Relativity

The Light Cone: An Illuminating Introduction to Relativity

Schwarzschild black holes (from The Light Cone -- source for Schwarzscild photo also ...).

Java Applet: Orbits in Strongly Curved Spacetime

C-ship: Relativistic ray traced images (special relativity illustrations)

Radius for Black Hole of a Given Mass
Object Mass Black Hole Radius
Earth 5.98 x 1027 g 0.9 cm
Sun 1.989 x 1033 g 2.9 km
5 Solar Mass Star 9.945 x 1033 g 15 km
Galactic Core 109 Solar Masses 3 x 109 km


Where Might We Find Black Holes?


It is impossible to observe a black hole directly and so any black hole candidates have to be identified by their effect on the matter surrounding them. If no other explanation for the observed phenomena is valid then it is likely that a black hole is present. There are some objects that are good candidates for the presence of a black hole.

  1. Any star shines and survives because the pull of gravity, which is trying to compress it, just balances the pressure generated by the nuclear furnace at its centre, which is trying to expand it. Once the furnace runs out of fuel, which must eventually happen, the pressure decreases, loses its battle with gravity, and the star collapses. Astronomers believe that one of only three things can happen to a star in this situation, depending on its mass. A star less massive than the Sun collapses until it forms a `white dwarf', with a radius of only a few thousand kilometers. If the star has between one and four times the mass of the Sun, it can produce a `neutron star', with a radius of just a few kilometers, and such a star might be recognised as a `pulsar'. The relatively few stars with greater than four times the mass of the Sun cannot avoid collapsing within their Schwarzschild radii and becoming black holes. So, black holes may be the corpses of massive stars.

  2. Most astronomers believe that galaxies like the Milky Way were formed from a large cloud of gas which collapsed and broke up into individual stars. We now see the stars packed together most tightly in the centre, or nucleus. It is possible that at the very centre there was too much matter to form an ordinary star, or that the stars which did form were so close to each other that they coalesced to form a black hole. It is therefore argued that really massive black holes, equivalent to a hundred million stars like the Sun, could exist at the centre of some galaxies.
Evidence for galactic size black holes may be found in the section on active galaxies.


Based on information in:
Science and Engineering Research Council
Royal Greenwich Observatory
Information Leaflet No. 9: `Blackholes'
webman@mail.ast.cam.ac.uk

How Might We See Black Holes?


Because black holes are small, and no signals escape from them, it might seem an impossible task to find them. However, the force of gravity remains, so if we detect gravity where there is no visible source of light then a black hole may be responsible. This type of argument, by itself, is not very convincing, and so we must look for other clues. If there is other material around a black hole which might fall into it, then it will. There is then a good chance that as it falls it will produce some detectable signal not from the black hole itself, but from just outside it.

Most stars are not single, like the Sun, but are found in pairs, small groups or large clusters. If a pair of stars have different masses then the more massive one will burn up its nuclear fuel and may become a black hole, whilst the other remains a normal star consuming its fuel more slowly. Gas can then be sucked from the star into the black hole. The gas becomes very hot, with a temperature of millions of degrees, and will shine not with visible light but with X-rays. These X-rays will have an observable effect on the light output from the ordinary star. Since the star and black hole go round each other every few days, we might expect to see regular variations in the brightness and X-ray output.

There are some X-ray sources which have all the properties described above. Unfortunately it is impossible to distinguish between a black hole and a neutron star unless we can prove that the mass of the unseen component is too great for a neutron star. Strong evidence was found by Royal Greenwich Observatory astronomers that one of these sources called Cyg X-1 (which means the first X-ray source discovered in the constellation of Cygnus) does indeed contain a black hole. Things are rather different if there is a massive black hole in the centre of a galaxy. It is possible there for a star to be swallowed by the black hole. The pull of gravity on such a star will be so strong as to break it up into its component atoms, and throw them out at high speed in all directions. Some of the fragments will fall into the hole, increasing its mass, whilst others could produce an outburst of radio waves, light and X-rays. Evidence for such behavior may be found in the section on Active Galaxies.

This is just the behaviour which is observed in galaxies of the type called `Quasars' and may well be happening in a milder way in the centre of our own Milky Way.


Based on information in:
Science and Engineering Research Council
Royal Greenwich Observatory
Information Leaflet No. 9: `Blackholes'
webman@mail.ast.cam.ac.uk

Frame Dragging

One of the strangest predictions of the general theory of relativity concerning black holes is called frame dragging. For a rotating black hole, the theory predicts that space and time itself can be dragged by the rotating black hole. The adjacent figure shows an artist's conception of this idea (J. Bergeron, Sky & Telescope: get permission; Ref). Some recent data has been interpreted as supporting evidence for frame dragging around a black hole (Ref).

Summary

These ideas are very bizarre, and yet there is rather strong evidence that black holes exist, as predicted by the theory. If that is true, then singularities and event horizons probably exist too. It is less likely that naked singularities exist, and we have no experimental evidence for them, but they can't be ruled out based on our present understanding.


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