The vacuum solution of Einstein’s theory of general relativity provides a rotating metric with a ring singularity, which is covered by the inner and outer horizons and an ergo region. In this paper, we will discuss how ghost-free, quadratic curvature, infinite derivative gravity (IDG) may resolve the ring singularity. In IDG the nonlocality of the gravitational interaction can smear out the delta-Dirac source distribution by making the metric potential finite everywhere including at $r=0$. We show that the same feature also holds for a rotating metric. We can resolve the ring singularity such that no horizons are formed in the linear regime by smearing out a delta-source distribution on a ring. We will also show that the Kerr metric does not solve the full nonlinear equations of motion of ghost-free quadratic curvature IDG.

In this paper, we will study the complete equations of motion for a ghost-free quadratic-curvature infinite-derivative gravity. We will argue that within the scale of nonlocality, a Schwarzschild-type singular metric solution is not permissible. Therefore, the Schwarzschild-type vacuum solution which is a prediction in Einstein-Hilbert gravity may not persist within the region of nonlocality. We will also show that just quadratic-curvature gravity, without infinite derivatives, always allows Schwarzschild-type singular metric solution.