Reissner-Nordstrom Solution from Weyl Transverse Gravity

TL;DR

This paper demonstrates that the Reissner-Nordstrom black hole solution naturally arises in Weyl-transverse gravity coupled with electromagnetism, specifically in four dimensions, highlighting a unique dimensional property of this modified gravity theory.

Contribution

It shows that the Reissner-Nordstrom solution is a classical solution in Weyl-transverse gravity only in four dimensions, revealing a special dimensional dependence of this theory.

Findings

Reissner-Nordstrom metric is a solution in Weyl-transverse gravity in four dimensions.

The theory maintains invariance under Weyl transformations and volume-preserving diffeomorphisms.

The solution's validity is coordinate-dependent, specifically in Cartesian coordinates.

Abstract

We study classical solutions in the Weyl-transverse (WTDiff) gravity coupled to an electro-magnetic field in four space-time dimensions. 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 (perhaps even in the quantum regime). In particular, we find that only in four space-time dimensions, the charged Reissner-Nordstrom black hole metric is a classical solution when it is expressed in the Cartesian coordinate system.