Geometric inequalities in spherically symmetric spacetimes

TL;DR

This paper explores geometric inequalities in spherically symmetric spacetimes by incorporating quasi-local mass, specifically the Misner-Sharp mass, to derive new inequalities and gain deeper insights into black hole, cosmological horizons, and normal bodies.

Contribution

It introduces novel techniques that integrate quasi-local mass into geometric inequalities, extending previous results and providing new relations in spherically symmetric spacetimes.

Findings

Derived new inequalities involving quasi-local mass and area.

Revealed insights into black hole and cosmological horizon geometries.

Extended inequalities to normal bodies beyond horizons.

Abstract

In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner-Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.