Smarr integral formula of D-dimensional stationary spacetimes in Einstein-æther–Maxwell theory

Abstract

Using the Wald formalism, we investigate the thermodynamics of charged black holes in D-dimensional stationary spacetimes with or without rotations in Einstein-æther–Maxwell theory. In particular, assuming the existence of a scaling symmetry of the action, we obtain the Smarr integral formula, which can be applied to both Killing and universal horizons. When restricted to 4-dimensional spherically symmetric spacetimes, previous results obtained by a different method are re-derived. Keywords: Einstein-æther–Maxwell theory, Wald formalism, Smarr integral formula