Quasilocal Energy, Komar Charge and Horizon for Regular Black Holes

TL;DR

This paper investigates the properties of quasilocal energy and Komar charge in regular black holes, revealing conditions under which certain energy identities hold or fail, especially in the context of nonlinear electrodynamics and dilaton gravity.

Contribution

It provides a detailed analysis of the Brown-York quasilocal energy and its relation to the Komar charge for various static, spherically symmetric black holes, including those with nonlinear electrodynamics.

Findings

The energy identity holds for linear cases but not for nonlinear electrodynamics.

Relations between horizon and infinity quantities are established for nonlinear electrodynamics.

Extensions to dilaton gravity solutions are also discussed.

Abstract

We study the Brown-York quasilocal energy for regular black holes. We also express the identity that relates the difference of the Brown-York quasilocal energy and the Komar charge at the horizon to the total energy of the spacetime for static and spherically symmetric black hole solutions in a convenient way which permits us to understand why this identity is not satisfied when we consider nonlinear electrodynamics. However, we give a relation between quantities evaluated at the horizon and at infinity when nonlinear electrodynamics is considered. Similar relations are obtained for more general static and spherically symmetric black hole solutions which include solutions of dilaton gravity theories.