Quasilocal Energy For Black Hole In String Theory

The Brown-York quasilocal energies of some black holes in string theory are calculated and Martinez's conjecture, originally proposed for the Kerr black hole in general relativity, is explored in string theory.We first review all kinds of energy definitions and introduce the Brown-York formalism. Moreover, we deduce exactly the general expressions for the proper integral involved in the quasilocal energy for arbitrary stationary axsiymmetric spacetime. By using the expression, we consider the quasilocal energies of some static charged black holes (such as Garfinkle-Horowitz-Strominger (GHS) black hole, Gibbons-Maeda (GM) black hole, Garfinkle-Horne (GH) black hole) in string theory. We fhd that the energies have the following important properties: (1) the energies are positive and monoton-ically decrease to their Arnowitt-Deser-Misner (ADM) masses at spatial infinity; (2) The energies have the correct Newtionial limiting, and include the binding energies from the gravitation^ electrostatic charge and dilaton charge, respectively; (3) Martinez's conjecture is valid for such black holes.We then extend the calculation to the stationary axisymmet-ric Einstein-Maxwell-dilaton-axion black hole (in the slow-rotation approximation). We find that the behavior of this energy as a function of the boundary surface radius is similar to those of the static black holes, and that the energy at the horizon does reduce to the expression conjectured by Martinez. In particular, we find thatMartinez's conjecture is also applicable to the Kerr-Sen black hole. This is different from Bose-Naing's result that the quasilocal energy of the Kerr-Sen black hole does not yield Martinez's conjecture.Our results show that Martinez's conjecture is valid for black hole not only in Einstein gravity but also in string theory.