Perturbations of Kerr with approximate Killing spinors -- Wave version

TL;DR

This paper introduces a novel framework for analyzing non-linear perturbations of Kerr spacetime using approximate Killing spinors, enabling background-independent characterization and evolution of deviations from Kerr.

Contribution

It develops a new covariant approach based on approximate Killing spinors to study Kerr perturbations without relying on a fixed background solution.

Findings

Constructs quantities measuring deviation from Kerr

Derives evolution equations for these quantities

Provides approximations of Killing vectors, mass, and angular momentum

Abstract

In this paper we develop a new framework for non-linear perturbations of the Kerr spacetime. This is based on a characterization of the Kerr spacetime in terms of a Killing spinor. On the perturbed spacetime, one can construct an approximation of the Killing spinor. Based on this, a number of quantities are constructed measuring the deviation from Kerr. Evolution equations for these quantities are derived. Approximations of the Killing vectors, the mass and angular momentum parameters etc., are constructed along with a full set of equations for their derivatives. In this setting, we don't need a reference background solution. Instead, we covariantly construct the relevant structures on the perturbed spacetime itself. This can eliminate many issues and allow for a cleaner analysis.