Rotating Black Holes in Metric-Affine Gravity

TL;DR

This paper presents an exact stationary axially symmetric black hole solution in metric-affine gravity, incorporating torsion and nonmetricity, characterized by mass, angular momentum, and shear charge, which indicates Lorentz invariance violation.

Contribution

It introduces a novel exact black hole solution in metric-affine gravity that includes post-Riemannian structures and Lorentz invariance violation.

Findings

The solution generalizes Kerr-deSitter metrics with torsion and nonmetricity.

It identifies shear charge as a new parameter related to Lorentz violation.

The solution advances understanding of black holes in alternative gravity theories.

Abstract

Within the framework of metric-affine gravity (MAG, metric and an independent linear connection constitute spacetime), we find, for a specific gravitational Lagrangian and by using {\it prolongation} techniques, a stationary axially symmetric exact solution of the vacuum field equations. This black hole solution embodies a Kerr-deSitter metric and the post-Riemannian structures of torsion and nonmetricity. The solution is characterized by mass, angular momentum, and shear charge, the latter of which is a measure for violating Lorentz invariance.