Generalizes Ricci flow to brane flows with n-forms, proves monotonicity for fixed field-dependent volume flows and that steady solitons are gradient solitons, including a new functional for Chern-Simons cases.
Black holes and branes in string theory
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abstract
This is a set of introductory lecture notes on black holes in string theory. After reviewing some aspects of string theory such as dualities, brane solutions, supersymmetric and non-extremal intersection rules, we analyze in detail extremal and non-extremal 5d black holes. We first present the D-brane counting for extremal black holes. Then we show that 4d and 5d non-extremal black holes can be mapped to the BTZ black hole (times a compact manifold) by means of dualities. The validity of these dualities is analyzed in detail. We present an analysis of the same system in the spirit of the adS/CFT correspondence. In the ``near-horizon'' limit (which is actually a near inner-horizon limit for non-extremal black holes) the black hole reduces again to the BTZ black hole. A state counting is presented in terms of the BTZ black hole.
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Brane flows
Generalizes Ricci flow to brane flows with n-forms, proves monotonicity for fixed field-dependent volume flows and that steady solitons are gradient solitons, including a new functional for Chern-Simons cases.