Bounds for axially symmetric linear perturbations for the extreme Kerr black hole

TL;DR

This paper derives simple integral bounds for axially symmetric linear perturbations of the extreme Kerr black hole, leading to pointwise bounds outside the horizon, which enhances understanding of black hole stability.

Contribution

It introduces new integral bounds based on conserved energies for perturbations of the extreme Kerr black hole, providing explicit pointwise estimates.

Findings

Integral bounds for perturbations established

Pointwise bounds outside the horizon derived

Enhanced understanding of black hole stability

Abstract

We obtain remarkably simple integral bounds for axially symmetric linear perturbations for the extreme Kerr black hole in terms of conserved energies. From these estimates we deduce pointwise bounds for the perturbations outside the horizon.