Introduction

Definition:

A Black Hole in a Binary system

A black hole is a region of space into which matter has collapsed and out of which light may not escape. There are two main types-the Schwarzschild black hole that does not rotate and the Kerr black hole that does. Unlike the prediction by the eighteenth century French mathematician Pierre Simon de Laplace, who used ordinary Newtonian physics, a black hole has a very sharp boundary in space known as the event horizon.

Event horizons are regions around gravitational singularities where infinite red shifts and infinite time dilation can occur. In the table 9 you can see what some of the gravitational time dilation effects look like as you get closer and closer to the mathematical limit of the event horizon of a very massive black hole. If you fall into a black hole, you will see nothing dramatic happen at the horizon, and, assuming you can survive the gravitational tidal stresses trying to pull you apart, you can enter the black hole after only a few seconds of your spaceship's time. To a distant observer, however, a much longer span of time than just a few seconds would appear to pass. But to actually get the highest time dilation factors, you would have to be less than a metre away from the event horizon, and by then both you and the distant observer would agree that you are at the horizon for any practical purpose of defining your condition.

There is a precise mathematical prediction of the radius of this horizon, which for objects that do not rotate depends only on the mass of the object that has collapsed through its event horizon. For every unit of mass equal to that of the Sun, the radius grows by 2.7 kilometres. The most massive black holes known are a billion times the mass of Sun and are as big as our entire solar system.

Scientists today call such an object a black hole. Though the history of the term is interesting, the main reason is that no light can escape from inside a black hole: it has, in effect, disappeared from the visible universe. Most physicists believe the existence of black hole, basing their views on a growing body of observations. In fact, present theories of how the cosmos began rest in part on Einstein's work and predict the existence of both singularities and the black holes that contain them. Yet Einstein himself vigorously denied their reality, believing, as did most of his contemporaries that black holes were a mere mathematical curiosity. He died in 1955, before the term "black hole" was coined or understood and observational evidence for black holes began to mount.

Formation:

A black hole is a simple object that has only a "center" and a "surface".

Imagine a dying star too massive to become either a white dwarf or a neutron star. The overpowering weight of the star's burned-out matter presses inward from all sides, causing the star to contract rapidly. As the star's matter becomes compressed to enormous densities, the strength of gravity at the surface of this rapidly shrinking sphere also increases dramatically. According to the general theory of relativity, distortions of space and time around the star become increasingly pronounced, and light rays emitted from the star's surface followed curved paths rather than straight lines (Figure above). Finally, the escape speed from the dying star's surface equals the speed of light. Because light cannot escape from the star, the star disappears. At this stage, space becomes so severely curved that, in a sense, a hole is punched in the fabric of the universe. The dying star disappears into this cavity. Leaving behind only a black hole.

(refer to the figure above)

A. The curvature of space around a main-sequence, giant, or supergiant star is so small that photons emitted from the star's surface travel in essentially straight lines.

B. At the surface of a collapsing neutron star, however, the surface gravity is very strong and the curvature of space is appreciable. Hence, photons emiitted from the star's surface follow curved paths.

C. As the star continues to collapse, the curvature of the surrounding space increases and the trajectories actually curve back to the star's surface.

D. When the neutron star shrinks to a certain critical size, the surrounding space is so highly curved that none of the emitted photons can escape. Thus, the star appears black, which is why it is callled a black hole.

(Photons emitted directly upward from the surface continue to follow a straight path, but these photons undergo an infinite gravitational red shift and therefore disappear.)

Structure:

A black hole is a simple object that has only a "center" and a "surface".

Imagine a dying star too massive to become either a white dwarf or a neutron star. The overpowering weight of the star's burned-out matter presses inward from all sides, causing the star to contract rapidly. As the star's matter becomes compressed to enormous densities, the strength of gravity at the surface of this rapidly shrinking sphere also increases dramatically. According to the general theory of relativity, distortions of space and time around the star become increasingly pronounced, and light rays emitted from the star's surface followed curved paths rather than straight lines (Figure: Formation of a Black Hole). Finally, the escape speed from the dying star's surface equals the speed of light. Because light cannot escape from the star, the star disappears. At this stage, space becomes so severely curved that, in a sense, a hole is punched in the fabric of the universe. The dying star disappears into this cavity. Leaving behind only a black hole.

Figure above sketches the geometry of space around a black hole. Note that space far from the hole is flat, because gravity is weak there. Near the hole, however, gravity is strong and the curvature of space is severe.
Surrounding a black hole, where the escape speed from the hole equals the sped of light, is the event horizon. This sphere is also sometimes thought of as the "surface" of this black hole, although the black hole's mass all lies well within this surface. Once a massive dying star collapses to within its event horizon, it disappears permanently from the universe. The term "event horizon" is in fact quite appropriate, because this surface is like a horizon beyond which we cannot see any events.
Once a dying star has contracted inside its event horizon, no forces in the universe can prevent the complete collapse of the star down to a single point. The star's entire mass is crushed to zero volume - and hence infinite density - at this point, known as singularity, at the center of the black hole. We can now see that the structure of a non-rotating black hole is quite simple. As sketched in Figure below, it has only two parts: a singularity, or center, and the event horizon, or surface, that surrounds it.

The Structure of a Nonrotating Black Hole

A nonrotating black hole has only two parts: a singularity, where all of the mass is located, and a surrounding event horizon. The distance from the singularity to the event horizon is called the Scharzschild radius (Rsch). Inside the event horizon, the escape speed exceeds the speed of light, so the event horizon is a one-way surface. Things can fall in, but nothing can get out.

The Structure of a Rotating Black Hole

A rotating black hole is surrounded by a region called the ergosphere, where the dragging of space and time around the hole is so severe that nothing can remain at a fixed location. Because the ergosphere is outside the event horizon, this bizarre region is accessible to us, and astronauts or asteroids could travel through it without disappearing into the black hole. According to detailed calcaulations, objects grazing the ergosphere could be catapulted back out into space at tremendous speeds. In other words, the ejected object could leave the ergosphere with more energy than it had initially, having extracted added energy from the hole's rotation. This is called the Penrose process, after Roger Penrose, the British mathematiciam who purposed it.

The structure of a black hole can be desribed with only three numbers.

In addition to shielding us from singularities, the event horizon prevents us from ever knowing much about anything that falls into a black hole. For example, there is no way we could ever discover the chemical composition of a massive star whose collapse has produced a particular black hole. Even if someone were to go into a black hole and make a measurement or conduct a chemical test, there is no way the observer could get any of his information back to the outside world. A black hole is, in fact, an "information sink". Many properties of matter falling into a black hole, such as its chemical composition, texture, shape, color, size, and shape, would simply vanish as soon as the matter crosses the horizon.
Because this information has completely vanished, it cannot affect the structure or properties of the hole. For example, consider two hypothetical black holes, one made from the gravitational collapse of 10 (FORMULA) of iron and the other made from the gravitational collapse of 10 (FORMULA) of peanut butter. Obviously, quite different substances went into the creation of the two holes. Once the event horizons of these two black holes have formed, however, both the iron and peanut butter will have permanently disappeared from the universe. As seen from the outside, the two holes are absolutely identical, making it impossible for us to tell which ate the peanut butter and which ate the iron. A black hole is thus unaffected by the information it destroys.

Because the black hole is indeed an information sink, it is reasonable to wonder whether we can determine anything all about the black hole. In other words, what properties characterize a black hole?

First, we can measure the mass of a black hole. One way to do this is would be by placing a satellite into orbit about the hole. After measuring the size and period of the satellite's orbit, we could use Newton's form of Kepler's third law to determine the mass of the black hole. This mass is equal to the total mass of all the material that has gone into the black hole.

Second, we can also measure the total electric charge possessed by the black hole. Like gravity, the electric force acts over long distances - it is a long-range interaction that is felt in space around the hole. Appropriate equipment on a space probe passing near the hole could measure the intensity of the of the electric field, and the electric charge could thus be determined.

In actuality, we would not expect a black hole to possess much, if any, electric charge. For example, if a hole did happen to start off with a sizable positive charge, it would vigorously attract vast numbers of negative charged electrons from the interstellar medium, which would soon neutralize the hole's charge. For this reason, astronomers usually neglect electric charge when discussing real black holes.

Although a black hole might theoretically have a tiny electric charge, it can have no magnetic field of its own whatsoever. When a black hole is created, however, the collapsing star from which it forms may possess an appreciable magnetic field. The star must therefore radiate this magnetic field away before it can settle down inside its event horizon. Theory predicts that the star does this by emitting electromagnetic and gravitational waves. As described in "The general theory of relativity" section, gravitational waves are ripples in the overall geometry of space. Some physicists are exploring the possibility of observing creation of black holes by detecting bursts of gravitational radiation emitted by collapsing massive stars (refer to "Gravitational waves" section)

Third, we can detect the effects of a black hole's rotation. Specifically, we can measure a black hole's angular momentum. An object's angular momentum is related to how fast it rotates and how the object's mass is distributed over its volume. As a dead star collapses into a black hole, its rotation naturally speeds up as its mass moves toward the center, just as a figure skater rotates faster when she pulls her arms and legs in. Hence, we expect black hole that forms from a rotating star to be spinning rapidly. Einstein's theory makes the startling prediction that this rotation causes space and time to be dragged around the hole. A spinning black hole is thus surrounded by space that rotates with the hole. In fact, around the event horizon of every rotating back hole, a region where this dragging of space and time is so severe that it is impossible to stay in the same place. No matter what you do, you get pulled around the hole, along with the rotating geometry of space and time. This region, here it is impossible to be at rest, is called the ergosphere.

To measure a black hole's angular momentum, we could hypothetically place two satellites in orbit around the hole. Suppose that one satellite circles the hole in the same direction the hole rotates and the other in the opposite direction. One satellite is thus carried along by the geometry of space and time, but the other constantly fighting its way "upstream." The two satellites will thus have different orbital periods. By comparing these two periods, astronomers can deduce the total angular momentum of the hole.

These three properties - mass, charge, and angular momentum - are the only ones that a black hole possesses. This simplicity is the essence of the famous no-hair theorem, first formulated in the early 1970's: "Black holes have no hair." Any and all additional properties carried by the matter that has fallen into the hole have disappeared from the universe and thus can have no effect on the structure of the hole.

Location:

Certain binary star systems probably contains black holes

Are there any black holes out there? Many astronomers think so, but finding black holes in the sky is a difficult business. Because light cannot escape from inside the event horizon, you cannot observe a black hole directly in the way that you can observe a star or planet. The best you can hope for is to detect the effects of a black hole's powerful gravity.

Close binary star systems offer the best chance of finding black holes in our Galaxy. For example, if the gravitational attraction of a black hole captured gas from its companion star, the fate of this material might reveal the existence of the hole. In fact, since the early 1970s, several good black hole candidates have been discovered in just this way.

Shortly after the launch of the Uhuru X-ray-detecting satellite, astronomers became intrigued with an X-ray source designated Cygnus X-1. Unlike pulsating X-ray sources, which emit regular bursts of X-rays every few seconds, the emissions from Cygnus X-1 are highly variable and irregular. Its X-ray emission flickers on time scales and that are as short as one-hundredth of a second. One of the fundamental concepts in physics is that nothing can travel faster than the speed of light. Because of this limitation, an object cannot flicker faster than the time required for light to travel across the object. Because light travels 3000 kilometers in a hundredth of a second, Cygnus X-1 must be smaller then the Earth.
Cygnus X-1 occasionally emits radio radiation, and in 1971 radio astronomers used these outbursts to show that the source was at the same location in the sky as the star HDE 226868 (Figure ------------>). Spectroscopic observations revealed that HDE 226868 is a B0 super giant with a surface temperature of about 31000 K. Because such stars do not emit significant amounts of X-rays, HDE226868 alone cannot be the X-ray source signals X-1. Because binary stars are very common, astronomers began to suspect the visible stars and the X-ray source are in orbit around each other.

Further spectroscopic observations soon showed that the spectral lines in the spectrum of HDE 226868 shift back and forth with a period of 5.6 days. This behavior is characteristic of a single-line spectroscopic binary; the companion HDE 226868 is just too dim to produce its own sets of spectrum lines. The clear implication is that HDE 226868 and Cygnus X-1 are the two components of a binary star system.

From the mass-luminosity relation, HDE 226868 is estimated to have a mass of roughly 30 (INSERT FORMULA). As a result, the unseen member of the binary system must have a mass of about 7 (INSERT FORMULA) or more. Otherwise it would not exert enough gravitational pull to make the B0 star wobble by the amount deduced from the periodic Doppler shifting of its spectral lines. Because 7 solar masses are too large for either a White dwarf or a neutron star, Cygnus X-1 is likely to be a black hole.

Energy:

Black holes spell trouble. Their arrival on the physics scene in the 1960s called for a radical rethink of several time- honoured ideas. For example when matter disappears into a black hole, less matter is necessarily left behind. Black holes could operate as a kind of cosmic vacuum cleaner, keeping the Universe heat and tidy. But this violates a sacred physics law that says that, left to itself, the Universe prefers disorder called "entropy".

This paradox was resolved when the fertile mind of Stephen Hawking probed deeply into black hole ideas in the early 1970s. While nobody can get inside information on a black hole, the event horizon, the frontier where light becomes trapped, does give some clues to the hole's appetite. When matter is sucked in, the hole gets heavier and its event horizon gets bigger. Hawking's new ideas suggested to Jacob Bekenstein at Princeton that the event horizon is a measure of the invisible disorder lurking inside.
Then came another problem. Entropy is intimately linked with temperature. If a black hole had entropy, it should also have a temperature. But to have a temperature, a body must radiate. Even black holes had to emit something. On a trip to Moscow in 1973, Hawking was convinced in discussions with Soviet cosmologists that the conundrum could be resolved with the wizardry of quantum theory.

According to the uncertainty principle, even a total vacuum is not empty, but full of quantum fireworks powered by "borrowed" energy. In quantum terms, energy is lent free of charge as long as it is paid back quickly enough -before Nature has time to notice.

HOLES THAT EXPLODE

When such a quantum blip happens near a black hole, the energy bookkeeping is affected by the huge gravitational force. If both particles fall into the black hole, nobody is any wiser. But if only one particle falls in, the black hole can absorb the energy debt and the other particle is suddenly free. To someone watching the black hole from afar, it looks as though the hole has radiated a particle.

Swallowing the energy debt reduces the mass of the black hole, according to Einstein's E=mc^2, so a black hole is continually "evaporating" -getting smaller and hotter. However, the rate of evaporation of normal black holes, formed by the collapse of stars, is negligible. With a temperature of less thana millionth of a degree above absolute zero, radiation is practically non-existent.

In 1971, early :in the black hole game, Hawking boldly suggested that in the immediate aftermath of the Big Bang, isolated concentrations of temperature and pressure could have formed much smaller black holes, as small as 10-13 centimetres (inches) across, about the size of a proton, but still weighing many millions of ton(ne)s. Hawking's calculations also showed that black hole temperature is inversely proportional to the mass -the smaller the black hole, the higher its temperature and the more it radiates. Small black holes should therefore be easier to see than big ones!

Finally microscopic hole will come to an end in a massive explosion. Many of these primordial "mini black holes" have probably already evaporated, disappearing in a gigantic shower of gammarays; others are nearing the ends of their lives and could soon die in a crescendo of radiation. Experimepts have looked for these flashes, but no convincing signal has yet been seen.

Evaporating black hole (figure on the right side): Quantum uncertainty allows pairs of particles and anti-Particles to pop out of empty space right outside the border of a black hole. One member of a pair may fall into the hole, while the other escapes ("Hawking radiation"). As black holes emit particles in this way they lose mass and size, eventually disappearing.