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

Abstract

In this paper we construct a linearized metric solution for an electrically charged system in a ghost-free infinite derivative theory of gravity which is valid in the entire region of spacetime. We show that the gravitational potential for a point-charge with mass $m$ is nonsingular, the Kretschmann scalar is finite, and the metric approaches conformal flatness in the ultraviolet regime where the nonlocal gravitational interaction becomes important. We 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 argue that the cosmic censorship conjecture is not required in this case. Unlike in the case of the Reissner-Nordstr\"om metric in general relativity, where $|Q|\ensuremath{\le}m/{M}_{p}$ must always be satisfied, in ghost-free infinite derivative gravity $|Q|>m/{M}_{p}$ is also allowed, such as for an electron.