Towards non-singular metric solutions in ghost-free nonlocal gravity

In this short paper we study how black hole singularities can be tackled in the context of nonlocal ghost-free gravity, in which the action is characterized by the presence of non-polynomial differential operators containing infinite order covariant derivatives. The ghost-freeness condition can be preserved by requiring that such nonlocal operators are made up of exponential of entire functions, thus avoiding the emergence of extra unhealthy poles in the graviton propagator. We will mainly focus on how infinite order derivatives can regularize the singularity at the origin by making explicit computations in the linear regime. In particular, we will show that this kind of non-polynomial operators can smear out point-like distribution and that the Schwarzschild metric can not be a solution of the field equations in the ghost-free infinite derivative gravity.