Reissner–Nordström solution from Weyl transverse gravity

Abstract

We study classical solutions in the Weyl-transverse (WTDiff) gravity coupled to an electromagnetic field in four spacetime dimensions. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeomorphisms (transverse diffeomorphisms) and is known to be equivalent to general relativity at least at the classical level (perhaps even in the quantum regime). In particular, we find that only in four spacetime dimensions, the charged Reissner–Nordström black hole metric is a classical solution when it is expressed in the Cartesian coordinate system.