On the stability operator for MOTS and the 'core' of Black Holes

TL;DR

This paper explores the stability operator for marginally outer trapped surfaces (MOTS) in black holes, introduces the concept of a 'core' of a black hole, and discusses how to extend results from spherical symmetry to general spacetimes.

Contribution

It introduces the 'core' of a black hole and proposes a new approach to analyze MOTS stability in general spacetimes using a novel eigenvalue formula.

Findings

In spherical symmetry, the marginally trapped tube forms the boundary of a core.

A new formula for the principal eigenvalue of the stability operator is proposed.

Potential extension of results to non-spherical black-hole spacetimes.

Abstract

Small deformations of marginally (outer) trapped surfaces are considered by using their stability operator. In the case of spherical symmetry, one can use these deformations on any marginally trapped round sphere to prove several interesting results. The concept of 'core' of a black hole is introduced: it is a minimal region that one should remove from the spacetime in order to get rid of all possible closed trapped surfaces. In spherical symmetry one can prove that the spherical marginally trapped tube is the boundary of a core. By using a novel formula for the principal eigenvalue of the stability operator, I will argue how to pursue similar results in general black-hole spacetimes.