New spinorial approach to mass inequalities for black holes in general relativity

TL;DR

This paper introduces a novel spinorial method using an elliptic equation to derive geometric inequalities for black hole masses in general relativity, providing new bounds based on boundary conditions and MOTS properties.

Contribution

It presents a second order elliptic spinorial approach that allows boundary condition specification, leading to new mass inequalities involving MOTS in black hole systems.

Findings

Mass is bounded from below by an integral over MOTS depending on a free spinor.

New bounds on black hole mass in terms of MOTS inner expansion.

A formalism for 1+1+2 spinorial decomposition is developed.

Abstract

A new spinorial strategy for the construction of geometric inequalities involving the Arnowitt-Deser-Misner (ADM) mass of black hole systems in general relativity is presented. This approach is based on a second order elliptic equation (the approximate twistor equation) for a valence 1 Weyl spinor. This has the advantage over other spinorial approaches to the construction of geometric inequalities based on the Sen-Witten-Dirac equation that it allows to specify boundary conditions for the two components of the spinor. This greater control on the boundary data has the potential of giving rise to new geometric inequalities involving the mass. In particular, it is shown that the mass is bounded from below by an integral functional over a marginally outer trapped surface (MOTS) which depends on a freely specifiable valence 1 spinor. From this main inequality, by choosing the free data in an appropriate way, one obtains a new nontrivial bounds of the mass in terms of the inner expansion of the MOTS. The analysis makes use of a new formalism for the $1+1+2$ decomposition of spinorial equations.