Wavy way to the Kerr metric and the quantum nature of its ring singularity

TL;DR

This paper explores a novel derivation of the Kerr metric via colliding gravitational waves, examines the classical stability of related spacetime structures, and demonstrates that quantum effects can regularize the Kerr ring singularity.

Contribution

It provides an alternative derivation of the Kerr metric using colliding gravitational waves and shows quantum effects can heal the classical ring singularity.

Findings

Kerr metric can be derived from colliding gravitational waves.

Certain spacetime structures are transient black holes under stability conditions.

Quantum probe indicates the Kerr ring singularity is quantum regular.

Abstract

From inherent non-linearity two gravitational waves, unless they are unidirectional, fail to satisfy a superposition law. They collide to develop a new spacetime carrying the imprints of the incoming waves. Same behaviour is valid also for any massless lightlike field. As a result of the violent collision process either a naked singularity or a Cauchy horizon (CH) develops. It was shown by Chandrasekhar and Xanthopoulos (CX) that a particular class of colliding gravitational waves (CGW) spacetime is locally isometric to the Kerr metric for rotating black holes. This relation came to be known as the CX duality. Such a duality can be exploited as an alternative derivation for the Kerr metric as we do herein. Not each case gives rise to a CH but those which do are transient to a black hole state provided stability requirements are met. These classical considerations can be borrowed to shed light on black hole formation in high energy collisions. Their questionable stability and many other sophisticated agenda, we admit that await for a full - fledged quantum gravity. Yet, to add an element of novelty, a quantum probe is sent in the plane $\theta =\pi /2$ to the naked ring singularity of Kerr which develops for the overspinning case $(a>M)$ to test it from a quantum picture. We show that the spatial operator of the reduced Klein-Gordon equation has a unique self-adjoint extension. As a result, the classical Kerr`s ring singularity is healed and becomes quantum regular. Our poetic message of the paper is summarized as Let there be light that collide with might to disperse the night and create holes that are white