Microscopic Entropy of the Magnetised Extremal Reissner-Nordstrom Black Hole

TL;DR

This paper investigates the microscopic entropy of extremal Reissner-Nordstrom black holes in a magnetic universe using Kerr/CFT correspondence, successfully reproducing the Bekenstein-Hawking entropy through dual CFT methods.

Contribution

It extends Kerr/CFT analysis to magnetised extremal black holes, deriving the central charge and matching microscopic entropy with classical results.

Findings

Microscopic entropy matches Bekenstein-Hawking entropy.

Near horizon geometry is a warped product of AdS2 and S2.

Magnetic field deforms the black hole geometry.

Abstract

The extremal Reissner-Nordstrom black hole embedded in a Melvin-like magnetic universe is studied in the framework of the Kerr/CFT correspondence. The near horizon geometry can be written as a warped and twisted product of $AdS_2 \times S^2$, also in presence of an axial external magnetic field that deforms the black hole. The central charge of the Virasoro algebra can be extracted from the asymptotic symmetries. Using the Cardy formula for the microscopic statistical entropy of the dual two-dimensional CFT, the Bekenstein-Hawking entropy, for this charged and magnetised black hole, is reproduced.