Quasi-Local Mass near the Singularity, the Event Horizon and the Null Infinity of Black Hole Spacetimes

TL;DR

This paper investigates the behavior of various quasi-local mass measures near key geometric features of black hole spacetimes, providing insights into the physical properties at singularities, horizons, and infinity.

Contribution

It computes and analyzes the Hawking, Brown-York, and Liu-Yau masses in maximal spherically symmetric black hole solutions near singularities, horizons, and null infinity.

Findings

Quasi-local masses exhibit specific limiting behaviors near singularities.

Mass measures behave differently at the event horizon and null infinity.

Results enhance understanding of black hole internal and boundary properties.

Abstract

The behaviour of geometric quantities close to geometric pathologies of a spacetime is relevant to deduce the physical behaviour of the system. In this work, we compute the quasi-local mass quantities - the Hawking mass, the Brown-York mass and the Liu-Yau mass in the maximal extensions of the spherically symmetric solutions of the Einstein equations inside the black hole region, at the singularity, the event horizon, and the null infinity, in the limiting sense of a geometric flow.