  String theory can accommodate black holes with the black hole parameters
related to string moduli. It is a well known but remarkable feature that the
near horizon geometry of a large class of black holes arising from string
theory contains a BTZ part. A mathematical theorem (Sullivan's Theorem) relates
the three dimensional geometry of the BTZ metric to the conformal structures of
a two dimensional space, thus providing a precise kinematic statement of
holography. Using this theorem it is possible to argue that the string moduli
space in this region has to have negative curvature from the BTZ part of the
associated spacetime. This is consistent with a recent conjecture of Ooguri and
Vafa on string moduli space.
