Schwarzschild Solution from WTDiff Gravity

Abstract

We study classical solutions in the Weyl-transverse (WTDiff) gravity. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is known to be equivalent to general relativity at least at the classical level. In particular, we find that in a general space-time dimension, the Schwarzschild metric is a classical solution in the WTDiff gravity when it is expressed in the Cartesian coordinate system.