Energy Extraction, or Lack Thereof

TL;DR

This paper demonstrates that a positive-definite total energy exists for axisymmetric perturbations of Kerr and Kerr-Newman black holes, despite the complications introduced by the ergo-region, advancing the understanding of black hole stability.

Contribution

It shows the existence of a positive-definite total energy for axisymmetric perturbations in rotating black hole spacetimes, overcoming previous obstacles posed by the ergo-region.

Findings

Positive-definite total energy identified for axisymmetric perturbations.

Applicable to Maxwell, gravitational, and electrovacuum perturbations.

Enhances understanding of black hole stability in general relativity.

Abstract

The problem of stability of rotating black holes is the subject of a long standing research program since the 1960s and remains an unresolved problem in general relativity. A major obstacle in the black hole stability problem is that the energy of waves propagating through rotating black holes spacetimes is not necessarily positive-definite, due to the so called ergo-region. This is a serious complication that limits the efficacy of most mathematical techniques. In this Letter, we report that, despite the ergo-region, there exists a positive-definite \emph{total energy} for axisymmetric Maxwell, gravitational and electrovacuum perturbations of Kerr and Kerr-Newman black hole spacetimes.