Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity

TL;DR

This paper explores black hole solutions within a non-minimally coupled Weyl connection gravity framework, revealing unique features like non-vanishing scalar curvature and modified Reissner-Nordström solutions influenced by matter content.

Contribution

It introduces novel black hole solutions in a non-metricity setting with Weyl connection, highlighting differences from standard $f(R)$ theories and analyzing effects of matter coupling.

Findings

Black hole solutions with non-zero scalar curvature are found.

Vacuum Schwarzschild solutions differ from constant curvature cases.

Reissner-Nordström solutions require matter fields, not vacuum.

Abstract

Schwarzschild and Reissner-Nordstr{\o}m black hole solutions are found in the context of a non-minimal matter-curvature coupling with the Weyl connection, both in vacuum and in the presence of a cosmological constant-like matter content. This special case of non-metricity leads to black hole solutions with non-vanishing scalar curvature. Moreover, vacuum Schwarzschild solutions differ from the ones from a constant curvature scenario in $f(R)$ theories with the appearance of a coefficient in the term linear in r and a corrected "cosmological constant". Non-vacuum Shwarzschild solutions have formally the same solutions as in the previous case with the exception being the physical interpretation of a cosmological constant as the source of the matter Lagrangian as not a simple reparametrization of the $f(R)$ description. Reissner-Nordstr{\o}m solutions cannot be found in vacuum, but only in the presence of matter fields, such that the solutions also differ from the constant curvature scenario in $f(R)$ theories by the term linear in r and corrected/dressed charge and cosmological constant.