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, which is a modified form of the teleparallel equivalent of general relativity. This theory departs from Einstein’s general relativity through the introduction of a scalar gravitational susceptibility function S ( x ),

, which is a new phenomenological feature of the spacetime that vanishes in the general relativity 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

$$M/(1+S)$$ M / ( 1 + S )

, where M denotes the mass of the solution in the general relativity 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 Weitzenböck torsion at the Schwarzschild horizon.