Conformally-flat, non-singular static metric in infinite derivative
  gravity
  In Einstein's theory of general relativity the vacuum solution yields a
blackhole with a curvature singularity, where there exists a point-like source
with a Dirac delta distribution which is introduced as a boundary condition in
the static case. It has been known for a while that ghost-free infinite
derivative theory of gravity can ameliorate such a singularity at least at the
level of linear perturbation around the Minkowski background. In this paper, we
will show that the Schwarzschild metric does not satisfy the boundary condition
at the origin within infinite derivative theory of gravity, since a Dirac delta
source is smeared out by non-local gravitational interaction. We will also show
that the spacetime metric becomes conformally-flat and singularity-free within
the non-local region, which can be also made devoid of an event horizon.
Furthermore, the scale of non-locality ought to be as large as that of the
Schwarzschild radius, in such a way that the gravitational potential in any
metric has to be always bounded by one, implying that gravity remains weak from
the infrared all the way up to the ultraviolet regime, in concurrence with the
results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole
can now be potentially replaced by a non-singular compact object, whose core is
governed by the mass and the effective scale of non-locality.
