Non-singular metric for an electrically charged point-source in ghost-free infinite derivative gravity

TL;DR

This paper constructs a non-singular, ghost-free infinite derivative gravity solution for an electrically charged point source, showing finite curvature and conformal-flatness in the ultraviolet, with implications for cosmic censorship and charge-mass relations.

Contribution

It presents the first linearized, non-singular metric solution for a charged source in ghost-free infinite derivative gravity, extending the understanding of gravitational and electromagnetic interactions.

Findings

The gravitational potential is non-singular and finite.

The metric approaches conformal-flatness in the ultraviolet regime.

The solution allows for charge-to-mass ratios beyond classical limits.

Abstract

In this paper we will construct a linearized metric solution for an electrically charged system in a {\it ghost-free} infinite derivative theory of gravity which is valid in the entire region of spacetime. We will show that the gravitational potential for a point-charge with mass $m$ is non-singular, the Kretschmann scalar is finite, and the metric approaches conformal-flatness in the ultraviolet regime where the non-local gravitational interaction becomes important. We will show that the metric potentials are bounded below one as long as two conditions involving the mass and the electric charge are satisfied. Furthermore, we will argue that the cosmic censorship conjecture is not required in this case. Unlike in the case of Reissner-Nordstr\"om in general relativity, where $|Q|\leq m/M_p$ has to be always satisfied, in {\it ghost-free} infinite derivative gravity $|Q|>m/M_p$ is also allowed, such as for an electron.