Statistical Entropy of Magnetic Black Holes from Near--Horizon Geometry

TL;DR

This paper investigates the near-horizon geometries of four-dimensional magnetic black holes derived from supergravity, enabling microscopic entropy counting that matches geometric entropy calculations.

Contribution

It demonstrates the near-horizon geometries as products of $AdS_3$ or BTZ black holes with $S^2$, facilitating statistical entropy analysis of magnetic black holes.

Findings

Exact agreement between statistical and geometric entropy.

Microstates are localized in the near-horizon region.

Near-horizon geometry is $AdS_3\times S^2$ for extremal and BTZ$\times S^2$ for non-extremal black holes.

Abstract

Four-dimensional magnetic black holes including dilaton and abelian gauge fields which are solutions of supergravity can also be obtained by dimensional reduction of the Einstein-Maxwell gravity in five dimensions. In the extremal case the five-dimensional solutions have horizon and their near-horizon geometry is $AdS_3\times S^2 $. In the non-extremal case the near-horizon geometry is shown to be the product of the three-dimensional Ba\~nados-Teitelboim-Zanelli black hole and $S^2$. This allows to perform microscopic counting of statistical entropy of magnetic black holes. Exact agreement with the geometric entropy is found. The microstates responsible for statistical entropy are located in the near-horizon region.