Kerr-Bertotti-Robinson Spacetime and the Kerr/CFT Correspondence

TL;DR

This paper establishes a Kerr/CFT correspondence for extremal Kerr--Bertotti--Robinson black holes, showing that their entropy can be exactly reproduced via a dual conformal field theory, even with external electromagnetic fields.

Contribution

It constructs the Kerr/CFT duality for Kerr--BR black holes, incorporating external electromagnetic fields and deriving the associated Virasoro algebra and entropy.

Findings

The near-horizon geometry is a warped AdS3 with an aligned Maxwell field.

The asymptotic symmetry algebra yields a Virasoro algebra with a field-dependent central charge.

The Cardy formula reproduces the black hole entropy for all admissible external field strengths.

Abstract

We construct the Kerr/CFT correspondence for extremal Kerr--Bertotti--Robinson (Kerr--BR) black holes, which are exact stationary solutions of the Einstein--Maxwell equations describing a rotating black hole immersed in a uniform Bertotti--Robinson electromagnetic universe. After reviewing the geometry, horizon structure, and thermodynamics of the Kerr--BR family, we demonstrate that the external field non-trivially modifies both the horizon positions and the extremality condition. For extremal configurations, the near-horizon limit yields a warped $\mathrm{AdS}_3$ geometry with an associated Maxwell field aligned to the $U(1)$ fibration. Imposing standard Kerr/CFT boundary conditions, the asymptotic symmetry algebra gives rise to a Virasoro algebra with central charge $c_L$ and left-moving temperature $T_L$ that depend explicitly on the external field strength. The Cardy formula then reproduces exactly the Bekenstein--Hawking entropy of the extremal Kerr--BR black hole for any admissible value of the Bertotti--Robinson field, thereby establishing a consistent Kerr/CFT dual description. Comparisons with the magnetized Melvin--Kerr and Kaluza--Klein black holes are briefly discussed, highlighting qualitative differences in their curvature profiles and horizon geometries.