Three Roads To Quantum Gravity

190 THREE ROADS TO QUANTUM GRAVITY
String theorists have found that in certain very special cases
black holes could be made by bringing together a collection of
these branes. To do this they make use of a feature of string
theory, which is that the gravitational force is adjustable. It is
given by the value of a certain physical ®eld. When this ®eld
is increased or decreased, the gravitational force becomes
stronger or weaker. By adjusting the value of the ®eld it is
possible to turn the gravitational force on and off. To make a
black hole they begin with the gravitational ®eld turned off.
Then they imagine assembling a set of branes which have the
mass and charge of the black hole they want to make. The
object is not yet a black hole, but they can turn it into one by
turning up the strength of the gravitational force. When they
do so a black hole must form.
String theorists have not yet been able to model in detail the
process of the formation of the black hole. Nor can they study
the quantum geometry of the resulting black hole. But they
can do something very cute, which is to count the number of
different ways that a black hole could be formed in this way.
They then assume that the entropy of the resulting black hole
is a measure of this number. When they do the counting, they
get, right on the nose, the right answer for the entropy of the
black hole.
So far only very special black holes can be studied by this
method. These are black holes whose electric charges are
equal to their mass. This is to say that the electrical
repulsions of two of these black holes are exactly balanced
by their gravitational attractions. As a result, one can put two
of them next to each other and they will not move, for there is
no net force between them. These black holes are very special
because their properties are strongly constrained by the
condition that their charge balances their mass. This makes
it possible to get precise results, and, when this is possible
the results are very impressive. On the other hand, it is not
known how to extend the method to all black holes. Actually,
string theorists can do a bit better than this, for the methods
can be used to study black holes whose charges are close to
their masses. These calculations also give very impressive
results: in particular, they reproduce every last factor of 2 and