Despite the monumental scientific discovery of General Relativity by Albert Einstein in 1915, few scientists wanted to accept Einstein and his final stroke in extending Newton’s foundations of classical physics. Einstein's work not only changed the way scientists looked at the world, but it also changed the consequences of physical law. Many physicists still wrestle with topics Einstein debated over 70 years ago. One of the most exotic questions of Einstein’s legacy deals with the possibility of the black hole. Few of Einstein’s contemporaries were willing to even consider its existence out of pure disregard for such an anomaly of science. However, one man, Karl Schwarzschild, was curious enough to see what Einstein’s Relativity predicted for stars. His findings would ultimately lead to a debate which has puzzled scientists and science fiction writers for decades.
In 1908, shortly after Einstein discovered the Special Theory of Relativity, Hermann Minkowski proved spacetime to be a four dimensional “fabric” that results when space and time are unified. Einstein’s law of spacetime warpage, the Einstein Field Equation, states that “mass and pressure warp spacetime.” Einstein’s General Theory of Relativity was therefore a new theory of gravity in that it proved that spacetime warpage and tidal gravity are the same phenomenon. Einstein proved that spacetime warpage causes freely falling particles, which are initially moving parallel, to consequently move together or apart along "geodesics," or the shortest possible paths along curved planes. Thus gravity is merely a manifestation of a curved entity of spacetime, dependent on the mass and pressure of the matter causing the curvature. (1)
Schwarzschild calculated Einstein’s field equations for the spacetime outside of any spherical star, known as the Schwarzschild Geometry. His calculations predicted a space which is so curved that Euclidean laws of mathematics cease to exist: the circumference to diameter ratio of a circle will not equal 3.14 and the sum of the interior angles of triangles will not equal 180 degrees. (2) He not only calculated the warpage of space, but he also calculated the warpage of time near the star. Schwarzschild’s solution described time dilation near a gravitating object; time flows more slowly at the star’s surface than far away. (3) As a result of the warpage of time, the light emitted from the star is affected by the disparity in time flow. The frequency of the light of the star is governed by the time flow at the origin of the light. Therefore, light emerging from atoms on a star’s surface will have a lower frequency than when the light reaches Earth. This is known as gravitational redshifting, because light emitted from a star, shifts towards the red end of the spectrum due to the lower frequency.
Schwarzschild's results were not real surprises to the scientific community of the 1920’s. However, the shocks came when the extremities of the results were hypothesized. Most scientists agreed that the more dense or compact a star is, the greater the warpage of its spacetime and the larger the redshift must be. The extremity of this case concerned the limit of the star’s circumference.
In 1783, a British philosopher, John Michell predicted the nature of compact stars. He realized that every gravitating object had an “escape velocity,” or the velocity necessary for anything to escape the gravitational pull of the body. (Earth has an escape velocity of about 617 km per sec.) The escape velocity of an object is directly related to the circumference of the body in that the smaller the circumference, the closer the body’s surface is to its center, an thus the greater the escape velocity must be to escape the pull of gravity. (4) Michell reasoned that there exists a critical circumference, where the escape velocity equals the speed of light. If the circumference was any smaller, even light cannnot escape.
Jumping to the 1920’s, Michell’s idea of escape velocity reemerged in the realm of Schwarzschild's solutions to Einstein's field equations. Scientists pondered over the ramifications of combining Schwarzschild’s solutions and Michell’s critical circumference. If a star had the critical circumference, then Schwarzschild’s solutions yielded very bizarre results. These "Shwarzschild Singularities," a.k.a. black holes, have very peculiar properties: Because time dilation is related to the density of a star, a star with a critical circumference will have infinitely dilated time. Thus the wavelength of light from the star will be infinitely shifted at the surface of the star and consequently infinitely redshifted to an observer on Earth which would remove all the light’s energy and cause it to cease to exist. (5) The star’s light would never reach Earth; it would be completely black. Furthermore, at no height above the event horizon (the boundary for a Shwarzschild Singularity) could anyone see emerging light; it would be lost from the universe, questioning the conservation of energy and mass. Time to an observer outside of the horizon would seemingly stop at the horizon of the star. Consider an example: If an astronaut was descending to the event horizon of a Shwarzscild Singularity with a watch that sent pulses to an outside observer every second, the gap between the pulses would increase gradually until eventually the gap would become infinitely spaced. Suppose the astronaut was to enter the critical circumference at precisely 9:00. At 8:59:58 sec, the gap to 8:59:59 sec would not take one second, but more like 130 seconds. The final second (8:59:59 to 9:00) would never reach the outside observer because time is infinitely dilated and thus the pulse will take an infinite amount of time to reach the observer. Also, the observer will see the astronaut get progressively closer to the event horizon, but will never see the astronaut actually enter. This is because the last ray of light from the astronaut will take an infinite amount of time to reach the observer. So even if the astronaut was inside the Singularity for 100 days, the observer will still see the astronaut as not having entered. Nobody in the scientific community was willing to believe in such things, especially Einstein. He wrote numerous papers as to why the SS could never exist, stating that they did not “smell right.” Thus the products of Einstein's own work were being challenged by Einstein himself. It would take many more years and extensive research in star death to realize that there exists a large chance that SS do indeed exist.
In order to understand star death, one must understand the life processes of a star. A star is formed when a large amount of gas (mostly hydrogen) begins to collapse on itself due to its gravitational attraction. As it contracts, the gas begins to collide more frequently and thus the gas heats up. As the gas continues to heat, the collisions begin to produce so much heat that helium is formed when the hydrogen collides. (6) The extra heat will also increase the pressure of the gas until it balances the contraction forces of its own gravity. Eventually, the star will run out of helium “gas” and its gravity will cause it to contract. The star then relies on other forces to restrain its gravity. (7) Stars with roughly the circumference of the earth, and the mass of the sun, called white dwarfs, rely on their subatomic particles to resist gravity. As the star contracts, the space inside contracts as well. The electrons inside of the star are thus confined to smaller and smaller areas and thus shake violently. This vioelent shaking is called electron degeneray pressure. (8) This pressure of the electrons resists the gravitational contraction of the star unless the star is so massive that the gravitational inward pull is even too great for the electron degeneracy pressure. A man named Subramanyan Chandrasekhar realized this limit. He deduced that if a star’s mass was greater than 1.4 times the mass of Earth's sun, (1.4 solar masses), then in order for electron degeneracy pressure to resist the gravitational contraction, the electrons would have to travel faster than light, which is impossible. Thus Chandrasekhar discovered the fact that white dwarfs could not exceed 1.4 solar masses.
The Chandrasekhar limit on white dwarfs gave Shwarzschild Singularities a greater chance for existence because it implied that not all stars were destined for the white dwarf graveyard. The big question of the existence of black holes therefore concerned stars with even larger circumferences than the Chandrasekhar limit. Physicists wondered what would happen to a star with such a large gravitational contraction force that no electron degeneracy pressure could stop. If there did not exist a pressure great enough to stop the gravitational force of stars larger than 1.4 solar masses, then Shwarzschild Singularities would have to exist since nothing was strong enough to stop the star's implosion. Thus the star would continue to contract until it reached the critical circumference and ultimately formed a black hole.
By the mid-1930’s, physicists desperately searched for another force which could stop the gravitational force of stars larger than 1.4 solar masses. It would take the genius of a man named Fritz Zwicky to discover the next degeneracy pressure for stars whose electron degeneracy pressure was not strong enough. Stars with masses greater than 1.4 solar masses will continue to contract through the futile electron degeneracy pressure. When the electrons cannot resist the gravity of the star any longer, they are forced to break free and pair with the star’s protons, thereby creating neutrons. The neutrons will then begin to shake violently causing what is known as neutron degeneracy pressure. The density in these neutron stars is so high that only neutrons can exist. (9) Thus the task of physicists was the same with white dwarfs; to find the possibility of a maximum mass of neutron stars. For if there existed a maximum mass for neutron stars, black holes would then still be able to exist when stars with even greater densities and masses than neutron stars collapsed. Ultimately, it was the combined work of Zwicky, John Wheeler, Robert Oppenheimer and George Volkoff, which lead to the discovery that there indeed was a maximum mass for neutron stars. By trial and error processes, Oppenheimer created a number of scenarios with successively heavier stars to see if neutron degeneracy pressure could resist gravity. When he found a star whose degeneracy pressure was great enough, he would experiment with an even heavier star until he found one whose degeneracy pressure could not hold. He and Volkoff discovered that neutron stars could not resist gravity when the star’s mass was greater than 2-3 solar masses. (10)
The final question still remains to be answered even after almost 70 years of research: can black holes exist? Their existence is not certain due to merely mass restrictions on the degeneracy pressure. Presently, there exists two theories of what may happen to stars in order to avoid the fate of becoming a black hole. The first is the idea that a contracting star ejects most of its mass through supernova explosions while contracting so to drop below 1.4 solar masses and therefore rest as a white dwarf forever. The other theory is that there exists yet another stellar graveyard for stars in addition to white dwarfs and neutron stars. Although neither theory can be corroborated easily, the possibility of black holes became so great that even Einstein began to wonder at their probable being.
Citations
1.Thorne, Kip S. Black Holes and Time Warps. W.W. Norton and Co. 1995.
2.Hawking, Stephen W. Black Holes and Baby Universes and other essays. Bantam Books NY, 1993.
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4.Thorne, Kip S. Black Holes and Time Warps. W.W. Norton and Co. 1995.
5.Hawking, Stephen W. Black Holes and Baby Universes and other essays. Bantam Books NY, 1993.
6.Seeds, Michael A. Foundations of Astronomy. 1990 Edition. Wadsworth Publishing Co. Belmont, CA.
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10.Thorne, Kip S. Black Holes and Time Warps. W.W. Norton and Co. 1995.
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