BTZ black holes and the near-horizon geometry of higher-dimensional black holes

Abstract

We investigate the connection between the BTZ black holes and the near-horizon geometry of higher-dimensional black holes. Under mild conditions, we show that (i) if a black hole has a global structure of the type of the non-extremal Reissner-Nordstrom black holes, its near-horizon geometry is $AdS_2$ times a sphere, and further (ii) if such a black hole is obtained from a boosted black string by dimensional reduction, the near-horizon geometry of the latter contains a BTZ black hole. Because of these facts, the calculation of the Bekenstein-Hawking entropy and the absorption cross-sections of scalar fields is essentially reduced to the corresponding calculation in the BTZ geometry under appropriate conditions. This holds even if the geometry is not supersymmetric in the extremal limit. Several examples are discussed. We also discuss some generalizations to geometries which do not have $AdS$ near the horizon.