Illustrated Theory of Everything: The Origin and Fate of the Universe by Stephen Hawking Page B
Authors: Stephen Hawking
Tags: science, Philosophy, Cosmology, Mathematics, Physics, Astrophysics & Space Science, Physics (General)
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willappear to have been emitted from the black hole. The smaller the black hole,the less far the particle with negative energy will have to go before it becomesa real particle. Thus, the rate of emission will be greater, and the apparent tem-perature of the black hole will be higher.
The positive energy of the outgoing radiation would be balanced by a flow ofnegative energy particles into the black hole. By Einstein’s famous equationE = mc2, energy is equivalent to mass. A flow of negative energy into the blackhole therefore reduces its mass. As the black hole loses mass, the area of itsevent horizon gets smaller, but this decrease in the entropy of the black holeis more than compensated for by the entropy of the emitted radiation, so thesecond law is never violated.
BLACK HOLE EXPLOSIONS
The lower the mass of the black hole, the higher its temperature is. So as theblack hole loses mass, its temperature and rate of emission increase. It there-fore loses mass more quickly. What happens when the mass of the black holeeventually becomes extremely small is not quite clear. The most reasonableguess is that it would disappear completely in a tremendous final burst of emis-sion, equivalent to the explosion of millions of H-bombs.
A black hole with a mass a few times that of the sun would have a tempera-ture of only one ten-millionth of a degree above absolute zero. This is muchless than the temperature of the microwave radiation that fills the universe,about 2.7 degrees above absolute zero-so such black holes would give off lessthan they absorb, though even that would be very little. If the universe is des-
tined to go on expanding forever, the temperature of the microwave radiationwill eventually decrease to less than that of such a black hole. The hole willthen absorb less than it emits and will begin to lose mass. But, even then, itstemperature is so low that it would take about 1066years to evaporatecompletely. This is much longer than the age of the universe, which is onlyabout 1010 years.
On the other hand, as we learned in the last lecture, there might be primor-dial black holes with a very much smaller mass that were made by the collapseof irregularities in the very early stages of the universe. Such black holes wouldhave a much higher temperature and would be emitting radiation at a muchgreater rate. A primordial black hole with an initial mass of a thousand mil-lion tons would have a lifetime roughly equal to the age of the universe.Primordial black holes with initial masses less than this figure would alreadyhave completely evaporated. However, those with slightly greater masseswould still be emitting radiation in the form of X rays and gamma rays. Theseare like waves of light, but with a much shorter wavelength. Such holeshardly deserve the epithet black. They really are white hot, and are emittingenergy at the rate of about ten thousand megawatts.
One such black hole could run ten large power stations, if only we could har-ness its output. This would be rather difficult, however. The black hole wouldhave the mass of a mountain compressed into the size of the nucleus of anatom. If you had one of these black holes on the surface of the Earth, therewould be no way to stop it falling through the floor to the center of the Earth.It would oscillate through the Earth and back, until eventually it settled downat the center. So the only place to put such a black hole, in which one mightuse the energy that it emitted, would be in orbit around the Earth. And theonly way that one could get it to orbit the Earth would be to attract it thereby towing a large mass in front of it, rather like a carrot in front of a donkey.This does not sound like a very practical proposition, at least not in theimmediate future.
THE SEARCH FOR PRIMORDIALBLACK HOLES
But even if we cannot harness the emission from these primordial black holes,what are our chances of observing them? We could look for the gamma raysthat the primordial black holes emit
The positive energy of the outgoing radiation would be balanced by a flow ofnegative energy particles into the black hole. By Einstein’s famous equationE = mc2, energy is equivalent to mass. A flow of negative energy into the blackhole therefore reduces its mass. As the black hole loses mass, the area of itsevent horizon gets smaller, but this decrease in the entropy of the black holeis more than compensated for by the entropy of the emitted radiation, so thesecond law is never violated.
BLACK HOLE EXPLOSIONS
The lower the mass of the black hole, the higher its temperature is. So as theblack hole loses mass, its temperature and rate of emission increase. It there-fore loses mass more quickly. What happens when the mass of the black holeeventually becomes extremely small is not quite clear. The most reasonableguess is that it would disappear completely in a tremendous final burst of emis-sion, equivalent to the explosion of millions of H-bombs.
A black hole with a mass a few times that of the sun would have a tempera-ture of only one ten-millionth of a degree above absolute zero. This is muchless than the temperature of the microwave radiation that fills the universe,about 2.7 degrees above absolute zero-so such black holes would give off lessthan they absorb, though even that would be very little. If the universe is des-
tined to go on expanding forever, the temperature of the microwave radiationwill eventually decrease to less than that of such a black hole. The hole willthen absorb less than it emits and will begin to lose mass. But, even then, itstemperature is so low that it would take about 1066years to evaporatecompletely. This is much longer than the age of the universe, which is onlyabout 1010 years.
On the other hand, as we learned in the last lecture, there might be primor-dial black holes with a very much smaller mass that were made by the collapseof irregularities in the very early stages of the universe. Such black holes wouldhave a much higher temperature and would be emitting radiation at a muchgreater rate. A primordial black hole with an initial mass of a thousand mil-lion tons would have a lifetime roughly equal to the age of the universe.Primordial black holes with initial masses less than this figure would alreadyhave completely evaporated. However, those with slightly greater masseswould still be emitting radiation in the form of X rays and gamma rays. Theseare like waves of light, but with a much shorter wavelength. Such holeshardly deserve the epithet black. They really are white hot, and are emittingenergy at the rate of about ten thousand megawatts.
One such black hole could run ten large power stations, if only we could har-ness its output. This would be rather difficult, however. The black hole wouldhave the mass of a mountain compressed into the size of the nucleus of anatom. If you had one of these black holes on the surface of the Earth, therewould be no way to stop it falling through the floor to the center of the Earth.It would oscillate through the Earth and back, until eventually it settled downat the center. So the only place to put such a black hole, in which one mightuse the energy that it emitted, would be in orbit around the Earth. And theonly way that one could get it to orbit the Earth would be to attract it thereby towing a large mass in front of it, rather like a carrot in front of a donkey.This does not sound like a very practical proposition, at least not in theimmediate future.
THE SEARCH FOR PRIMORDIALBLACK HOLES
But even if we cannot harness the emission from these primordial black holes,what are our chances of observing them? We could look for the gamma raysthat the primordial black holes emit
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