Three Roads To Quantum Gravity

92 THREE ROADS TO QUANTUM GRAVITY
astrophysical black holes have temperatures of a very small
fraction of a degree. They are therefore much colder than the
2.7 degree microwave background. But a black hole of much
smaller mass would be correspondingly hotter, even if it were
smaller in size. A black hole the mass of Mount Everest would
be no larger than a single atomic nucleus, but it would glow
with a temperature greater than the centre of a star.
The radiation emitted by a black hole, called Hawking
radiation, carries away energy. By Einstein's famous relationship
between mass and energy, E = mc 2 , this means that the
radiation carries away mass as well. This implies that a black
hole in empty space must lose mass, for there is no other
source of energy to power the radiation it emits. The process
by which a black hole radiates away its mass is called black
hole evaporation. As a black hole evaporates, its mass
decreases. But since its temperature is inversely proportional
to its mass, as it loses mass it gets hotter. This will go on at
least until the temperature becomes so hot that each photon
emitted has roughly the Planck energy. At this point the mass
of the black hole is itself roughly equal to the Planck mass,
and its horizon is a few Planck lengths across. We have got
down to the regime where quantum gravity holds sway. What
happens to the black hole next could only be decided by a full
quantum theory of gravity.
The evaporation of an astrophysical black hole is a very
slow process. The evaporation rate, which depends on the
temperature, is very low because the temperature itself is so
low, initially. It would take a black hole the mass of the Sun
about 10 57 times the present age of the universe to evaporate.
So this is not something we are going to observe soon. But the
question of what happens at the end of black hole evaporation
is one that fascinates those of us who think about quantum
gravity. It is a subject in which it is easy to ®nd paradoxes to
mull over. For example, what happens to the information
trapped inside a black hole? We have said that the amount of
trapped information is proportional to the area of the horizon
of the black hole. When the black hole evaporates, the area of
its horizon decreases. Does this mean that the amount of
trapped information decreases as well? If not, then there