Reissner-nordström Anti-de Sitter Black Holes and Energy

We show that the tetrad field whose metric gives the Reissner-Nordström anti-de Sitter black holes gives the correct value of energy in Møller tetrad theory of gravitation. Mustafa et al. has derived a Reissner-Nordström anti-de Sitter black holes solution in Møller tetrad theory of gravitation [1]. Then, a calculations of energy of these black holes in the spherical polar coordinate have been carried out. The result of these calculations gives the energy in the form E = M − Q 2 r + r 3 l 2. (1) They discussed this results according to the results of the calculated energy given in the framework of general relativity. We have some comments on this discussion. First of all the calculations of energy that has been done in the spherical polar coordinate is not right because P µ used in these calculations is not transform as a 4-vector under a linear coordinate transformation [2]. The calculations will be more accurate in the Cartesian coordinate [3, 4, 5] and we have done such calculations and obtained the necessary components of the superpotential of Eq. (22) in Ref.[1]