Electrovacuum solutions in non-local gravity

TL;DR

This paper investigates non-local gravity coupled with electromagnetism, deriving perturbative corrections to Reissner-Nordström black holes and exploring implications for quantum effects on curved spacetimes.

Contribution

It introduces a Kaluza reduction approach to couple electromagnetism non-locally to gravity and develops an iterative method for solving the resulting equations perturbatively.

Findings

Real corrections exist between the inner and outer horizons of black holes.

Higher order corrections remain real and perturbative.

The approach may have implications for quantum effects on horizons.

Abstract

We consider the coupling of the electromagnetic field to a non-local gravity theory comprising of the Einstein-Hilbert action in addition to a non-local $R\, {\Box}^{-2} R$ term associated with a mass scale $m$. We demonstrate that in the case of the minimally coupled electromagnetic field, real corrections about the Reissner-Nordstr\"om background only exist between the inner Cauchy horizon and the event horizon of the black hole. This motivates us to consider the modified coupling of electromagnetism to this theory via the Kaluza ansatz. The Kaluza reduction introduces non-local terms involving the electromagnetic field to the pure gravitational non-local theory. An iterative approach is provided to perturbatively solve the equations of motion to arbitrary order in $m^2$ about any known solution of General Relativity. We derive the first-order corrections and demonstrate that the higher order corrections are real and perturbative about the external background of a Reissner-Nordstr\"om black hole. We also discuss how the Kaluza reduced action, through the inclusion of non-local electromagnetic fields, could also be relevant in quantum effects on curved backgrounds with horizons.