Near Horizon Extreme Magnetized Kerr Geometry

TL;DR

This paper explores the geometry of near horizon extreme magnetized Kerr black holes and their holographic duality to a two-dimensional conformal field theory, extending previous Kerr/CFT correspondence to include magnetic fields.

Contribution

It derives the near horizon geometry of extremal magnetized Kerr black holes and computes the transformed central charge within the Ernst-Papapetrou formalism, advancing the understanding of magnetized Kerr/CFT correspondence.

Findings

Derived the near horizon geometry of magnetized Kerr black holes.

Calculated the Ernst potentials for these geometries.

Obtained the transformed central charge for magnetized cases.

Abstract

The conjectured magnetized Kerr/CFT correspondence states that the quantum theory of gravity in the near horizon of extreme Kerr black holes immersed by the magnetic field, Near Horizon Extreme Magnetized Kerr black holes, is holographic dual to a two-dimensional chiral conformal field theory. To obtain Near Horizon Extreme Magnetized Kerr geometry, the extreme limit of the magnetized Kerr metric is taken so, $ a=M $ and then continued by transforming the coordinates to have a warped and twisted product of $ \textrm{AdS}_2 \times \textrm{S}^2 $, and also with the Near Horizon Extreme Kerr metric one. Consequently, we can obtain also the new Ernst potentials for those geometries. Finally, the transformed central charge from the extremal non-magnetized one to the magnetized one in the Ernst-Papapetrou formalism is obtained.