Gravity with perimeter action and gravitational singularities

We consider the perturbation of the Schwarzschild solution by the perimeter action. The asymptotic behaviour of the solution at infinity and at the horizon are calculated and analysed in the first approximation. In the regions far from the matter sources the perturbations are characterised by the ratio of the Plank length to the Schwarzschild radius and are infinitesimally small. At short distances the perturbation is large and there appears a space-time region of the Schwarzschild radius scale that is unreachable by test particles. These regions are located there where the standard theory of gravity has singularities. (C) 2021 The Author(s). Published by Elsevier B.V.