Page 57 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 7

Figure 7:4

To an observer at a distance, it will appear to have been emitted from the black hole. The smaller the black hole, the
shorter the distance the particle with negative energy will have to go before it becomes a real particle, and thus the
greater the rate of emission, and the apparent temperature, of the black hole.
The positive energy of the outgoing radiation would be balanced by a flow of negative energy particles into the black
2
hole. By Einstein’s equation E = mc (where E is energy, m is mass, and c is the speed of light), energy is proportional
to mass. A flow of negative energy into the black hole therefore reduces its mass. As the black hole loses mass, the
area of its event horizon gets smaller, but this decrease in the entropy of the black hole is more than compensated for
by the entropy of the emitted radiation, so the second law is never violated.

Moreover, the lower the mass of the black hole, the higher its temperature. So as the black hole loses mass, its
temperature and rate of emission increase, so it loses mass more quickly. What happens when the mass of the black
hole eventually becomes extremely small is not quite clear, but the most reasonable guess is that it would disappear
completely in a tremendous final burst of emission, 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 temperature of only one ten millionth of a degree
above absolute zero. This is much less than the temperature of the microwave radiation that fills the universe (about

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