Thermal properties of charged dilaton black hole, energy and momentum in teleparallel equivalent of general relativity

Two different charged dilaton black holes in 4-dimension, within teleparallel equivalent of general relativity (TEGR), are derived. These solutions are related through local Lorentz transformation. The total energy of these black holes, using three different methods, the Hamiltonian method, the translational momentum 2-form and the Euclidean continuation method given by Gibbons and Hawking, is calculated. It is shown that the three methods give the same results. The value of energy is shown to depend on the mass M and charge q. The verification of the first law of thermodynamics is proved. Finally, it is shown that if the charge q is vanishing then, the total energy reduced to that of Schwarzschild’s black hole.