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Black Hole Essay, Research Paper
An image of the core of the Whirlpool galaxy M51 taken by the Wide Field Planetary Camera onboard the Hubble Space Telescope. It shows an immense ring of dust and gas which is thought to surround and hide a giant black hole, 1 million times the mass of the Sun, in the center of the galaxy. The ring forms an accretion disc of gas, about 100 light years across, falling toward the black hole. The two brighter areas perpendicular to the widest dark lane are two jets of particles accelerated by the black hole.
Anyone who has ever watched the launch of a rocket is familiar with the concept that escape from a gravitational field requires the expenditure of energy. The stronger the gravitational field, more energy is required to escape from its clutches. If the rocket has insufficient fuel, it will return to Earth and escape is impossible. Thus, it is not hard to imagine a gravitational field strong enough to prevent the escape of any object with a finite amount of energy.
The gravitational force of an object is governed by a combination of the amount of matter it contains and its volume. The more the matter is confined in progressively smaller volume, the larger the gravitational field at the surface of the object. Since even a light beam has a finite amount of energy, one can imagine a massive object in a sufficiently small volume that would posses a gravitational field strong enough to prevent the escape of that light. The French mathematician Simon Laplace reasoned in 1795 that, if Newton’s corpuscular theory of light were correct, there could exist massive object from which light could not escape.
Indeed, any theory of gravity should contain the notion of such an object. In the case of Einstein’s theory of General Relativity, we call such an object a black hole.
However, in the case of general relativity, the path taken by a light beam defines the geometry of space-time for it represents the “shortest distance between two points.” Such a path is called a geodistic . Thus, for a black hole in general relativity, a light beam originating on the surface that cannot escape really travels nowhere. In some sense, all “surface” points can be viewed as the same point and the object can be said to have been sealed off from the ordinary space and time of outside observers. The point from which light can no longer escape is known as the event horizon since knowledge of events beyond that point can never be transmitted to the outside world by a light beam or any other mechanism. The event horizon imposes a form of censorship on the makeup of a black hole. Indeed, the only aspects of a black hole that may be ascertained from outside are its mass, net charge, and rate of spin. No internal processes that depend on time in any way can be detected in the external environment, for that would constitute sending signals from inside the black hole to the outside when not even light can escape. This “censorship” is what is responsible for the small number of measurable properties of the black hole itself-mass, spin, and charge.
While there are complications in defining the size of a black hole, one can uniquely specify its circumference and thus define a radius as just the circumference divided by 2. This radius is known as the Schwarzschild radius after Karl Schwarzschild, who first defined it as R s=2GM/c 2. Here M is the mass of the black hole, G is the Newtonian constant of gravity, and c is the speed of light. However, R s should not be viewed as the distance from the event horizon of the black hole to its center. The geometry of space-time in the interior of the black hole is so warped that Euclidean notions of distance no longer apply. Nevertheless, R s does provide a measure of the space around a particular mass M that will be seriously warped. R s for an object having the mass of the sun is about 3 km. Thus, to turn the Sun into a black hole, one would have to cram all of its mass into a sphere having about a 3 km radius. Squeezing any such mass into a volume dictated by its Schwarzschild radius posses a serious assembly problem. In fact, about the only processes which might lead to the formation of a black hole involve the death of moderately massive normal stars or the formation of supermassive stars.
As evolving stars exhaust the nuclear fuel which enables them to support their own weight and shine at the same time, they begin a rapid collapse. It is believed that the crushing self-gravity of the collapsing star may be sufficient to form a black hole with the mass of several times that of the Sun. Such black holes would have Schwarzschild radii of several to perhaps a few tens of kilometers. Considering their mass, they are really tiny things. If one were to replace the Sun with a black hole of the same mass as the Sun, there would be a region of space a few kilometers in size located where the center of the Sun currently resides where space would be extremely warped. However, the gravitational field of this object, measured at the distance of the Earth, would be exactly that of the present-day Sun. The Earth and planets would continue in their orbits and except for it being rather dark, the solar system would continue much as it does today. If one were to launch a rocket from the Earth to hit the black hole, the task would be immensely more difficult than hitting the Sun. The Sun presents a target nearly one and a half million kilometers across while the black hole would be more than one hundred thousand times smaller. This emphasizes just how difficult it is to feed matter into a black hole.
Normally, one must get within a few Schwarzschild radii in order to feel the major effects of the black hole. Indeed, one of the observational tests for the presence of a black hole in binary systems involves observing heated matter as it is unmercifully squeezed during its final plunge into the black hole. Such matter will emit fluctuating amounts of x rays as a result of being squeezed. The rate of fluctuation is tied to the size of the emitting region and we find in such systems that the x rays come from a volume of space only a few kilometers in size. These are the dimensions of the environment surrounding a black hole of stellar proportions. In several instances, further analysis of the orbital motion in the binary system indicates that the dark unseen member of the binary system is much more massive than the Sun. A dark stellar component more massive than the Sun confined to a volume smaller than a few kilometers is a prime candidate for a black hole.
There is at least one other situation where astronomers suspect the existence of a black hole. Again, since it does not radiate light, we must detect it through the effect its gravitational field has on neighboring objects. In the centers of some galaxies the stars, gas and dust of the galaxy are moving at very high speeds, suggesting they are being pulled about by the gravity of some very massive object. If the object was a collection of massive stars, it would shine so brightly as to dominate the light from the galactic center. The absence of light from the massive object suggests it is a black hole. In one active galaxy, the Hubble Space Telescope has even observed disks of matter that appear be accreting onto a central massive dark object which is likely to be a black hole. Recently a large team of astronomers reported the results of a worldwide study involving the Hubble Space Telescope, the International Ultraviolet Explorer satelites and many ground based telescopes which were able to detect light which was emitted by the accreting matter as it spirals into the black hole which was subsequently absorbed and re-emitted by the orbiting clouds just a few light-days away from the central source. Mass estimates of the central source determined from the motion of these clouds suggests that the object has a mass of at least several million times the mass of the Sun. So much material contained in a volume of space no larger than a few light days provides the best evidence yet for the existence of a black hole at the center of this galaxy.
The concept of massive black holes at the centers of some galaxys is supported by theoretical investigations of the formation of very massive stars. Stars of more than about one hundred times the mass of the Sun cannot form because they will explode from nuclear energy released during their contraction before the star can shrink far enough for its self-gravity to hold it together. However, if cloud of interstellar material collapsing to form a star contains about a million time the mass of the Sun, the collapse will occur so fast that the nuclear processes initiated by the collapse will not stop the collapse and disrupt the star. The collapse will continuum unrestrained until the object formed is a black hole with a mass a million times the mass of the Sun or more.
Such objects appear to be required to understand the behavior of the material in the center of some galaxys. Indeed, it seems likely that black holes may reside at the centers of normal galaxies such as our own Milky Way. Again, the best evidence comes from the motion of gas clouds near the galactic center. However, the presence of a black hole at the center of our own galaxy is further supported by the observation of certain energetic gamma rays emanating from the galactic center. The origin of these rays requires an extremely energetic environment such as is found in the immediate neighborhood of a black hole.
All that has been said so far involves black holes as described by the general theory of relativity. However, in the realm of the very small, quantum mechanics has proved to be the proper theory to describe the physical world. To date, no one has successfully combined general relativity with quantum mechanics to produce a fully self consistent theory of quantum gravity. However, in 1974 someone suggested that an application of quantum principles to a black hole showed that it would radiate energy like a perfect radiator having a temperture inversely proportional to its mass. While the amount of radiation for any astrophysical black hole is pathetically small, the possibility of it happening at all was revolutionary. It suggested the first link between quantum theory and general relativity and has spawned a host of new ideas which expand the relationship between the two theories. It represents a classical example of a concept which may have little if any direct practical application, but revolutionizes the way in which we view the physical world. Binary System
Any system of two stellar-like objects which orbit one another under the influence of their combined gravity.
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