Mayer's Formula for Black Hole Thermodynamics in Constant Magnetic Field

Aims/ objectives: Using the concepts of the classical thermodynamics, we calculated in this work, the thermodynamic potential of black holes in the presence of a constant externel magnetic field present in the surrounding black hole. This calculation takes into account the developments previously provided by (Hawking, Bekenstein, Davies and Straumann) on the equations governing the dynamics of black holes,with an arbitrary value of the surface gravity k. Like the four classical thermodynamic Maxwell equations, we have developed, for black holes, new twenty four fundamental equations. Among these equations, particular attention was given to the calculation of specific heats CΩ,Φ,M and CJ,Q,B and the Mayer formula for a black hole in the presence of magnetic field.