Bounds for the metric and shift vector on extreme Kerr under linear axially symmetric gravitational perturbations

TL;DR

This paper derives integral bounds for the shift vector and metric perturbations in extreme Kerr black holes under linear, axially symmetric gravitational disturbances, advancing towards precise pointwise bounds.

Contribution

It introduces integral estimates for the shift and metric in the maximal isothermal gauge for linear perturbations of Minkowski and extreme Kerr spacetimes, including the horizon.

Findings

Integral bounds for shift and metric perturbations established.

Includes bounds that encompass the horizon in extreme Kerr.

Progress towards pointwise bounds for perturbations.

Abstract

We present integral estimates for the shift and induced metric in the maximal isothermal gauge, corresponding to linear axially symmetric gravitational perturbations over the Minkowski and extreme Kerr metric. These bounds are a step towards finding pointwise bounds for the perturbations. In particular the presented estimate for the shift includes the horizon for the extreme Kerr case.