String Theory and M-Theory

Black holes in string theory 551
direction. However, a complete resolution of the information loss puzzle
undoubtedly requires understanding how string theory makes sense of the
singularity, where quantum gravity effects become very important. So it
is fair to say that this is still an open question.
• Can string theory elucidate the thermodynamic description of black holes?
Does black-hole entropy have a microscopic explanation in terms of a large
degeneracy of quantum states? One of the most important achievements
of string theory in recent times (starting with work of Strominger and
Vafa) is the construction of examples that provide an affirmative answer
to this question. This chapter describes explicit string solutions for which
a microscopic derivation of the Bekenstein–Hawking entropy is known.
• Are there black-hole solutions that correspond to single microstates rather
than thermodynamic ensembles? If so, do they have a singularity and a
horizon? Or do these properties arise from thermodynamic averaging?
These questions are currently under discussion. However, since the answers
are not yet clear, they will not be addressed further in this chapter.
• What, if anything, renders black-hole singularities harmless in string theory?
In some cases, as illustrated by the analysis of the conifold in Chapter
9, the singularity can be “lifted” once nonperturbative states are taken
into account. One natural question is whether string theory can elucidate
the status of the cosmic censorship conjecture?
• Does string theory forbid the appearance of closed time-like curves? Such
causality-violating solutions can be constructed. There needs to be a
good explanation why such solutions should or should not be rejected as
unphysical. It may be that they only occur when sources have unphysical
properties.
• What generalizations of black-hole solutions exist in dimensions D > 4?
The case of five dimensions is discussed extensively in this chapter, and explicit
supersymmetric black-hole solutions are presented. Black holes fall
into two categories: (1) large black holes that have finite-area horizons in
the supergravity approximation; (2) small black holes that have horizons
of zero area, and hence a naked singularity, in the supergravity approximation.
The small black holes acquire horizons of finite area when stringy
corrections to the supergravity approximation are taken into account. It
seems that large supersymmetric black holes only arise for D ≤ 5. This is
one reason why there has been a lot of interest in the D = 5 case. Another
reason is that nonspherical horizon topologies become possible for D > 4.
The example of D = 5 black rings will be described.
Chapter 12 describes black p-brane solutions. Black branes are higher-