The mass formula for quasi-black holes

TL;DR

This paper derives a mass formula for static quasi-black holes, revealing a perfect parallel with black hole mass formulas and showing that extremal cases have zero surface stress contribution, highlighting electromagnetic mass origin.

Contribution

It establishes a detailed mass formula for quasi-black holes and demonstrates their mass parallels with black holes despite different derivations.

Findings

Mass formula for quasi-black holes matches that of black holes.

Extremal quasi-black holes have zero surface stress contribution.

Total mass can have a pure electromagnetic origin.

Abstract

A quasi-black hole, either non-extremal or extremal, can be broadly defined as the limiting configuration of a body when its boundary approaches the body's quasihorizon. We consider the mass contributions and the mass formula for a static quasi-black hole. The analysis involves careful scrutiny of the surface stresses when the limiting configuration is reached. It is shown that there exists a strict correspondence between the mass formulas for quasi-black holes and pure black holes. This perfect parallelism exists in spite of the difference in derivation and meaning of the formulas in both cases. For extremal quasi-black holes the finite surface stresses give zero contribution to the total mass. This leads to a very special version of Abraham-Lorentz electron in general relativity in which the total mass has pure electromagnetic origin in spite of the presence of bare stresses.