(explanation of this Penrose diagram)

Black holes turn out to be important "laboratories" in which to test string theory, because the effects of quantum gravity turn out to be important even for large macroscopic holes. Black holes aren't really "black" since they radiate! Using semi-classical reasoning, Stephen Hawking showed black holes emit a thermal spectrum of radiation at their event horizon. Since string theory is, among other things, a theory of quantum gravity, it should be able to describe black holes in a consistent way. In fact there are black hole solutions which satisfy the string equations of motion. These equations of motion resemble the equations of general relativity with some extra matter fields coming from string theory. Superstring theories also have some special black hole solutions which are themselves supersymmetric, in that they preserve some supersymmetry.

One of the most dramatic recent results in string theory is the derivation
of the **Bekenstein-Hawking entropy** formula for black holes obtained
by counting the microscopic string states which form a black hole. Bekenstein
noted that black holes obey an "area law", dM = K dA, where 'A' is the
area of the event horizon and 'K' is a constant of proportionality. Since
the total mass 'M' of a black hole is just its rest energy, Bekenstein realized that this is similar to the thermodynamic
law for entropy, dE = T dS. Hawking later performed a semiclassical calculation
to show that the temperature of a black hole is given by T = 4 k [where
k is a constant called the "surface gravity"]. Therefore the entropy
of a black hole should be written as **S = A/4**.
Physicists Andrew Strominger and Cumrin Vafa,
showed that this exact entropy
formula can be derived microscopically (including the factor of 1/4) by
counting the degeneracy of quantum states of configurations of strings
and D-branes which correspond to black holes in
string theory. This is compelling evidence that
D-branes can provide a short distance
weak coupling description of certain black holes! For example, the
class of black holes studied by Strominger and Vafa are described by 5-branes,
1-branes and open strings traveling down the 1-brane all wrapped on a 5-dimensional
torus, which gives an effective one dimensional object -- a black hole.

Hawking radiation can also be understood in terms of the same configuration,
but with open strings traveling in both directions. The open strings
interact, and radiation is emitted in the form of closed strings.
The system decays into the configuration shown above.

Explicit calculations show that for certain types of supersymmetric
black holes, the string theory answer agrees with the semi-classical supergravity
answer including non-trivial frequency dependent corrections called *greybody
factors*. This is more evidence that string theory is a consistent and
accurate fundamental theory of quantum gravity.

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