Spherical symmetric fields on torsion-free Palatini Gauss-Bonnet theory

TL;DR

This paper investigates spherically symmetric solutions in a four-dimensional torsion-free Palatini Gauss-Bonnet gravity theory, revealing complex equations and unexpected hidden gauge symmetries beyond known transformations.

Contribution

It demonstrates the existence of hidden gauge symmetries in the spherically symmetric sector of the theory, which are beyond standard diffeomorphisms and Weyl transformations.

Findings

Existence of hidden gauge symmetries in the theory

Complexity of the resulting field equations

Insights into the structure of Palatini Gauss-Bonnet gravity

Abstract

The Gauss-Bonnet density `a la Palatini' is not a total derivative in four dimensions. We study spherically symmetric fields for the torsion-free theory. The resulting equations are highly complicated but we show the existence of unexpected hidden gauge symmetries, beyond diffeomorphisms and Weyl transformations.