The quantization of a Kerr-AdS black hole

TL;DR

This paper develops a quantum gravity model for Kerr-AdS black holes, deriving solutions that interpret as radiation and gravitational waves, and shows the spacetime can be extended with a timelike singularity, avoiding the information paradox.

Contribution

It introduces a quantum gravity framework for Kerr-AdS black holes with equal rotational parameters, providing new solutions and insights into spacetime extension and singularity structure.

Findings

Solutions as products of stationary and temporal eigenfunctions

Event horizon as a Cauchy hypersurface allowing causal crossing

Maximal extension with a timelike curvature singularity

Abstract

We apply our model of quantum gravity to a Kerr-AdS spacetime of dimension $2 m+1$, $m\ge2$, where all rotational parameters are equal, resulting in a wave equation in a quantum spacetime which has a sequence of solutions that can be expressed as a product of stationary and temporal eigenfunctions. The stationary eigenfunctions can be interpreted as radiation and the temporal as gravitational waves. The event horizon corresponds in the quantum model to a Cauchy hypersurface that can be crossed by causal curves in both directions such that the information paradox does not occur. We also prove that the Kerr-AdS spacetime can be maximally extended by replacing in a generalized Boyer-Lindquist coordinate system the $r$ variable by $\rho=r^2$ such that the extended spacetime has a timelike curvature singularity in $\rho=-a^2$.