Modified gauge invariant Einstein Maxwell gravity and Thermodynamic phase transition of anti de Sitter ReissnerNordstrom black holes

Abstract

By contracting Ricci tensor of metric field with electromagnetic tensor field we make a scalar term added with the Einstein-Maxwell (EM) gravity Lagrangian density and then obtain modified Reissner Nordstrom (RN) black hole metric via perturbation method. In fact our motivation in use of this alternative gravity theory instead of the EM gravity is based on influence of cosmic magnetic field throughout the space time as inevitable effect at duration of cosmic inflation. Our goal in this work is investigation of contribution of this interaction term on the Hawking temperature and possibility of phase transitions too.