Schwarzschild Spacetime and the Local Limit of Nonlocal Gravity

Abstract

We investigate static spherically symmetric solutions within the framework of the local limit of nonlocal gravity. This theory departs from Einstein's general relativity (GR) through the introduction of a scalar gravitational susceptibility function $S(x)$, $1+S > 0$, which is a new feature of the spacetime that vanishes in the GR limit. It is shown that the Schwarzschild spacetime constitutes an exact solution of the modified source-free gravitational field equations provided $S$ is a constant. The mass of the corresponding Schwarzschild solution is given by $M/(1+S)$, where $M$ denotes the mass of the solution in the GR limit. The interpretation of the solution in terms of a black hole is ruled out due to the divergence of the algebraic invariants of the Weitzenb\"ock torsion at the Schwarzschild horizon.