Black holes and branes in string theory

TL;DR

These notes review how black holes in string theory can be analyzed via the D-brane description of extremal cases and via dualities that connect non-extremal cases to the BTZ black hole times a compact space. The central approach combines D-brane microstate counting, U-duality, and near-horizon holography to reproduce the Bekenstein-Hawking entropy $S = A/(4 G_N)$ for extremal black holes and to map higher-dimensional black holes to BTZ-type geometries with invariant entropy and temperature. The analysis extends to the AdS/CFT framework, where the BTZ black hole is described by a dual conformal field theory and Cardy-like counting matches black hole entropy. The work thus provides a unified picture linking microscopic stringy degrees of freedom, dualities, and holographic descriptions across dimensions.

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.