Black Holes with Weyl Charge and Non-Riemannian Waves

TL;DR

This paper explores a modified gravity theory with non-Riemannian connections, revealing solutions with gravitational charges analogous to electromagnetic charges, and investigates gravitational waves coupled to spinor fields.

Contribution

It introduces a gauge-covariant field equation framework in non-Riemannian gravity and finds solutions with gravitational charges and coupled gravitational-spinor wave solutions.

Findings

Existence of gravitational charges similar to electromagnetic charges.

Solutions include a Reissner-Nordström-like metric with Weyl charges.

Presence of plane-symmetric gravitational waves coupled to spinor fields.

Abstract

A simple modification to Einstein's theory of gravity in terms of a non-Riemannian connection is examined. A new tensor-variational approach yields field equations that possess a covariance similar to the gauge covariance of electromagnetism. These equations are shown to possess solutions analogous to those found in the Einstein-Maxwell system. In particular one finds gravi-electric and gravi-magnetic charges contributing to a spherically symmetric static Reissner-Nordstr\"om metric. Such Weyl ``charges'' provide a source for the non-Riemannian torsion and metric gradient fields instead of the electromagnetic field. The theory suggests that matter may be endowed with gravitational charges that couple to gravity in a manner analogous to electromagnetic couplings in an electromagnetic field. The nature of gravitational coupling to spinor matter in this theory is also investigated and a solution exhibiting a plane-symmetric gravitational metric wave coupled via non-Riemannian waves to a propagating spinor field is presented.