Schwarzschild Solution from WTDiff Gravity

TL;DR

This paper demonstrates that the Schwarzschild solution, a fundamental black hole metric, also arises as a classical solution in Weyl-transverse (WTDiff) gravity, which is classically equivalent to general relativity but with additional symmetries.

Contribution

It shows that the Schwarzschild metric is a solution in WTDiff gravity across dimensions when expressed in Cartesian coordinates, highlighting the theory's classical equivalence to GR.

Findings

Schwarzschild metric is a solution in WTDiff gravity.

WTDiff gravity is invariant under Weyl transformations and volume-preserving diffeomorphisms.

The solution holds in general space-time dimensions.

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.