Black Holes Help (page 3)
Introduction to Black Holes
Some neutron stars, as they collapse under their own weight, apparently do not stop even when all the space has been removed from between the subatomic particles. If the mass of such a star is great enough, calculations show that gravitation will become so powerful that no other force in the Cosmos can overcome it, not even the forces within neutrons and other particles.
When a neutron star gets going on the runaway frenzy of gravitational collapse that nothing can stop, the object will, in theory, continue to shrink until it becomes a geometric point that contains all the mass of the neutron star from which it formed but zero volume. There is an overwhelming gravitational field at its “surface” and a slowing down of time (because of relativistic effects, to be dealt with in a later chapter) to a complete stop relative to the outside Universe. This object is called a space-time singularity .
Surrounding the singularity is a spherical zone within which nothing can escape, not even visible light or other EM radiation. It is a “zone of no return” because the escape velocity is greater than the speed of light in free space. The outer boundary of this zone is called the event horizon (Fig. 14-6). To an outside observer, the object would appear as a black sphere having the radius of the event horizon. The edge of the sphere would glow faintly because of starlight that has been almost, but not quite, captured and pulled in. The background of stars near such a black hole would appear distorted because of space warping caused by gravitation.
Gravity’s Ultimate Victory
From a simplistic standpoint, gravitation can become so powerful that it will not let anything escape, not even the energy packets called photons that represent all forms of EM radiation. As the gravitational field at the surface of a collapsing neutron star becomes increasingly powerful, EM rays are bent downward significantly as they leave the surface. At a certain point, the rays leaving in an almost horizontal direction fall back. The star continues to collapse, and the gravitational field becomes more powerful still; rays fall back at ever-increasing angles. When the radius of the object gets so small that the gravitational field at the surface reaches critical intensity, only those photons traveling straight up from the surface manage to get away. However, things don’t stop there. The collapsar keeps shrinking within the event horizon; then all photons are trapped. No known form of energy can propagate faster than photons, and so the event horizon represents a one-way membrane : Things can get in, but nothing can get out.
This idea is not new. As long as there has been a particle theory of light, imaginative scientists have theorized that black holes can exist. When Albert Einstein revolutionized physics with his theory of relativity in the early 1900s, new evidence arose for the existence of black holes. However, nobody had ever seen an object in space that fit the description. The nature of black holes, assuming that they exist, is such that they are invisible at all wavelengths. The fantastic nature of black holes, along with the apparent fact that they can never be observed directly, originally caused some scientists to scoff. How could we say, for example, that angels were not dancing on the surfaces of neutron stars that had collapsed to within their event horizons? After all, no one could take a look and disprove such an idea! Recently, however, most astronomers have come to believe that black holes are not only plausible but real. They’re out there.
The Schwarzchild Radius
There is a formula, based on the mass of an object, that allows us to calculate the radius to which any spherical object would have to be squashed in order for the surface to reach the event horizon. This radius is called the Schwarzchild radius , named after the astrophysicist Karl Schwarzchild who first came up with the formula in 1916. He based the derivation of his formula on the supposition that if an object got small enough, the energy of photons emitted from the surface of that object would not be sufficient to propel them out of its gravitational field. Sometimes the Schwarzchild radius is called the gravitational radius .
Suppose that an object has a mass M (in kilograms). Its Schwarzchild radius r (in meters) would depend directly on the mass. The greater the mass, the greater is the Schwarzchild radius. The formula is remarkably simple:
r = 2 GM / c 2
where c 2 is the speed of light squared (approximately 8.9875 × 10 16 m 2 /s 2 ) and G is a constant known as the gravitational constant , a characteristic of the Cosmos. The value of G has been measured by painstaking experimentation and has been found to be approximately 6.6739 × 10 –11 .
You are invited to perform some calculations with this formula if you like. Do you want to figure out the gravitational radius of your body? Remember, you must use your mass in kilograms to get the answer. You’ll come up with an exceedingly small value. You would not survive being crushed to such a submicroscopic size.
The Earth would have to be compressed to the size of a grape in order to fall within its Schwarzchild radius. The Sun would have to collapse to a radius of approximately 2.9 km (1.8 mi). It is believed that a star must originally have at least three solar masses to generate enough gravitational power, on its demise, to collapse into a black hole.
Apparently, our parent star, the Sun, will never achieve the dubious distinction of withdrawing from the Universe in a cocoon of its own gravitation. It’s not massive enough. This might bring to mind a new meaning of the old adage, “The bigger they are, the harder they fall.” Size does matter!
Warping Of Space
We ordinarily think of space as having three dimensions (height, width, and depth, for example). According to Einstein, however, three-space , as it is called, can be curved with respect to some fourth spatial dimension that we cannot see. We expect that rays of light in space should obey the rules of Euclidean geometry. One of the fundamental rules of light behavior, according to Newtonian physics, dictates that rays of light always travel in straight lines. Such a continuum is called Euclidean space . However, what if space is non-Euclidean ?
According to the theory of general relativity, space is distorted, or bent, by gravitation. The extent of this bending is insignificant at the Earth’s surface. It takes an enormously powerful gravitational field to cause enough bending of space for its effects to be observed as an apparent bending of light rays. However, the effect has been seen and measured in starlight passing close to the Sun during total solar eclipses, when the Sun’s disk is darkened enough so that stars almost behind it can be seen through telescopes. The light from certain distant quasi-stellar sources ( quasars ), when passing near closer objects having intense gravitational fields, has been seen to produce multiple images as the rays are bent.
The bending of space in the vicinity of a strong gravitational field has been likened to the stretching of a rubber membrane when a mass is placed on it. Suppose that a thin rubber sheet is placed horizontally in a room, attached to the walls at a height of, say, 1.5 m above the floor. This sheet is stretched until it is essentially flat. Then a small but dense object such as a ball of solid iron is dropped right in the middle of the sheet. It will be bent in a funnel-like shape. The curvature of the sheet will be greatest near the ball and will diminish with increasing distance from the ball. This is how astronomers believe that space is warped by intense gravitation (Fig. 14-7).
It’s easy to see how objects traveling through warped space can’t possibly go in straight lines: There are no straight paths within such a continuum. According to the theory of general relativity, real space is non-Euclidean every where because there are gravitational fields everywhere. In some regions of space, gravitation is weak, and in other places, it is strong. But there is no place in the Universe that entirely escapes the influence of this all-pervasive force.
Do Black Holes Really Exist?
There are plenty of stars that are more than three times the mass of the Sun. Astronomers agree that many of these stars have long since blown up, gone through their white dwarf phases, and presumably also gone through the collapsing process. This suggests that black holes comprise a significant proportion of the matter in the Universe.
As long as we can’t see them, we do not have a good way to find out if black holes exist. Fortunately, however, real black holes are not as black as theory implies. According to the research of the well-known cosmologist Stephen Hawking, black holes gradually lose their mass by emitting energy. This need not necessarily all be in the form of EM radiation; energy also can be lost as gravitational waves .
The idea of a gravitational wave was first made plausible when Einstein developed his general theory of relativity. Figure 14-8 is a simplified depiction of a gravitational wave as it leaves a black hole and travels through the space-time continuum. Just as a pebble, when dropped into a still pond, produces concentric, expanding, circular ripples in the two-dimensional surface of the water, so does the black hole produce concentric, expanding, spherical ripples in the three-dimensional continuum of space. Ripples are also produced in time—as hard as this might be to imagine!
Gravitational-wave detectors have been built in an effort to detect ripples in space and time as they pass. Because they involve the very fabric of the Cosmos, such waves can penetrate anything with no difficulty whatsoever. A gravitational disturbance coming from the nadir (straight down as you see it while standing upright) would be every bit as detectable as one coming from overhead.
As of this writing, no conclusive evidence of gravitational waves has been found. However, astronomers are reasonably confident that they exist. The challenge is nothing more (or less) than continuing to refine the detection strategy until ripples in space and time are discovered and can be attributed to some real, however bizarre, celestial object.
When we expand our scope of observation to an intergalactic scale, there is other evidence for the existence of black holes.
Practice problems of this concept can be found at: Extreme Objects in Our Galaxy Practice Problems
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