Can Martinez’s conjecture be extended to string theory?

Abstract

The universality of Martinez's conjecture, which states that the quasilocal energy of a black hole at the outer horizon reduces to twice its irreducible mass, or equivalently to $\sqrt{A/4\ensuremath{\pi}}$ $(A$ is the area of the black hole), is investigated by calculating Brown-York quasilocal energies for stationary black holes in heterotic string theory, e.g., for the stationary Kaluza-Klein black hole, the rotating Cveti\ifmmode \check{c}\else \v{c}\fi{}-Youm black hole, the stationary axisymmetric Einstein-Maxwell-dilaton-axion black hole, and the Kerr-Sen black hole. It is shown that Martinez's conjecture can be extended from general relativity to heterotic string theory since the quasilocal energies of these stationary black holes tend to their Arnowitt-Dener-Misner masses at spatial infinity, and reduce to $\sqrt{A/4\ensuremath{\pi}}$ at the event horizons.