Quasilocal energy for rotating charged black hole solutions in general relativity and string theory

TL;DR

This paper investigates the behavior of quasilocal energy in rotating charged black holes within general relativity and string theory, testing Martinez's conjecture and finding it holds for Kerr but not for Kerr-Sen black holes.

Contribution

The study extends the analysis of Martinez's conjecture to Kerr-Sen black holes in string theory, revealing its limitations beyond general relativity.

Findings

Martinez's conjecture holds for Kerr black holes at the horizon.

For Kerr-Sen black holes, the quasilocal energy does not match the conjectured value at the horizon.

The energy decreases monotonically with boundary radius, approaching the ADM mass at infinity.

Abstract

We explore the (non)-universality of Martinez's conjecture, originally proposed for Kerr black holes, within and beyond general relativity. The conjecture states that the Brown-York quasilocal energy at the outer horizon of such a black hole reduces to twice its irreducible mass, or equivalently, to \sqrt{A} /(2\sqrt{pi}), where `A' is its area. We first consider the charged Kerr black hole. For such a spacetime, we calculate the quasilocal energy within a two-surface of constant Boyer-Lindquist radius embedded in a constant stationary-time slice. Keeping with Martinez's conjecture, at the outer horizon this energy equals the irreducible mass. The energy is positive and monotonically decreases to the ADM mass as the boundary-surface radius diverges. Next we perform an analogous calculation for the quasilocal energy for the Kerr-Sen spacetime, which corresponds to four-dimensional rotating charged black hole solutions in heterotic string theory. The behavior of this energy as a function of the boundary-surface radius is similar to the charged Kerr case. However, we show that in this case it does not approach the expression conjectured by Martinez at the horizon.