On the energy of a charged dilaton black hole

Employing energy-momentum pseudotensor of Einstein, we obtian the energy distribution of a dyonic dilaton black hole. The energy distribution of this black hole depends on mass M , electric charge Qe, magnetic charge Qm and asymptotic value of the dilaton φ0. We also make some comparisons between the results of Virbhadra et. al. and ours. PASC:04.20.-q, 04.50,+h E-mail:[email protected] E-mail:[email protected] E-mail:[email protected] 1 Charged dilaton black hole solutions have been obtained by Grafinkle, Horowitz and Strominger(GHS solutions) [1]. They are static spherical symmetric black hole solutions of the dilaton gravity theory. In this theory the gravity is coupled to electromagnetic and dilaton fields and can be describled by the four-dimensional effective string action. The action can be expresses as I = ∫ dx √−g [ −R + 2(∇φ) + eF 2 ] . (1) In a peculiar coordinate form, GHS solutions have a singularity whose area is zero at r = Q 2 m M e0 . To characterize a gravitational point source, their choice of the coordinate system may not be the most appropriate one. Thus, Cheng, Lin and Hsu [2] use the standard spherical coordinate system which is more suitable for describling the structure of the charged dilaton black hole. They obtained the more general solutions which named the dyonic dilaton black hole solutions. GHS solutions were found to be the special cases of dyonic dilaton black hole solutions when electric or magnetic charges are switched off. For these special cases, two solutions are related by some coordinate transformations [2]. For example, The singularity r = Q 2 m M e0 of GHS solutions corresponds to the singularity r = 0 of the dyonic dilaton black hole solutions. Recently, Virbhadra et. al. [3] get the gravitational energy of charged dilaton black hole solutions. Based on the GHS solutions, they found a