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

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.