Demagnetizing KBR and New Ricci-flat Rotating Metric

TL;DR

This paper introduces a new Ricci-flat rotating metric derived from the Kerr solution, which modifies the asymptotic structure and preserves some thermodynamic properties despite lacking an asymptotically-flat region.

Contribution

It constructs a novel Ricci-flat metric by demagnetizing the KBR solution, providing a neutral seed for magnetizing Kerr black holes with preserved thermodynamic relations.

Findings

The new metric is a deformation of Kerr with a parameter B.

The first law of thermodynamics holds despite non-asymptotic flatness.

Some thermodynamic relations mirror those of Kerr black holes.

Abstract

We construct a new Ricci-flat metric by demagnetizing the recently reported Kerr-Bertotti-Robinson (KBR) solution. The metric is a deformation of the Kerr metric characterized by a parameter $B$, so that the asymptotic Kerr becomes a regular dome of spindle shape with north and south poles. Despite lacking an asymptotically-flat region, we find that the first law of black hole thermodynamics can be established. Some thermodynamic relations are identical to those of the Kerr black hole, as if the constant $B$ is absent. Our Ricci-flat rotating metric serves a neutral seed for a variety of inequivalent schemes of magnetizing the Schwarzschild and Kerr black holes.