Self-Renormalization of the Classical Quasilocal Energy

TL;DR

This paper introduces a method to evaluate the quasilocal energy inside black hole horizons, demonstrating it remains finite at the singularity and revealing energy concentration just inside the horizon.

Contribution

It provides a novel prescription for calculating quasilocal energy within black hole horizons, extending previous definitions to the interior region.

Findings

QLE is finite at the singularity for various black holes

Energy is concentrated just inside the horizon

The method extends quasilocal energy evaluation inside horizons

Abstract

Pointlike objects cause many of the divergences that afflict physical theories. For instance, the gravitational binding energy of a point particle in Newtonian mechanics is infinite. In general relativity, the analog of a point particle is a black hole and the notion of binding energy must be replaced by quasilocal energy. The quasilocal energy (QLE) derived by York, and elaborated by Brown and York, is finite outside the horizon but it was not considered how to evaluate it inside the horizon. We present a prescription for finding the QLE inside a horizon, and show that it is finite at the singularity for a variety of types of black hole. The energy is typically concentrated just inside the horizon, not at the central singularity.