Remarks on the stability operator for MOTS

TL;DR

This paper investigates the stability of marginally outer trapped surfaces (MOTS) using the stability operator, providing new formulas for eigenvalues, characterizing marginally outer trapped tubes, and discussing implications for black hole cores.

Contribution

It introduces novel formulas for the principal eigenvalue of the stability operator and characterizes the structure of MOTTs passing through a given MOTS.

Findings

New formulas for the principal eigenvalue of the stability operator

Characterization of marginally outer trapped tubes (MOTT)

Discussion on the concept of black hole 'core' in relation to MOTS

Abstract

Small deformations of marginally outer trapped surfaces (MOTS) are studied by using the stability operator introduced by Andersson-Mars-Simon. Novel formulae for the principal eigenvalue are presented. A characterization of the many marginally outer trapped tubes (MOTT) passing through a given MOTS is given, and the possibility of selecting a privileged MOTT is discussed. This is related to the concept of `core' of a black hole: 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 MOTT is the boundary of a core. I argue how similar results may hold in general spacetimes.