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

We explore the (non-)universality of Martinet'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 root A/2 root 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 Martinet's conjecture, at the outer horizon this energy equals root A/2 root pi 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 it does not approach the expression conjectured by Martinet at the horizon. [S0556-2821(99)06018-X].