Non-Singular Spherically Symmetric Solution in Einstein-Scalar-Tensor Gravity

Abstract

A static spherically symmetric metric in Einstein-scalar-tensor gravity theory with a scalar field potential $V[\varphi ]$ is non-singular for all real values of the coordinates. It does not have a black hole event horizon and there is no essential singularity at the origin of coordinates. The weak energy condition ${\rho }_{\varphi }>0$ fails to be satisfied for $r\lesssim 1.3r_S$ (where $r_S$ is the Schwarzschild radius) but the strong energy condition ${\rho }_{\varphi }+3p_{\varphi }>0$ is satisfied. The classical Einstein-scalar-tensor solution is regular everywhere in spacetime without a black hole event horizon. However, the violation of the weak energy condition may signal the need for quantum physics anti-gravity as $r\to 0$. The non-singular static spherically symmetric solution is stable against the addition of ordinary matter.

13 pages, 6 figures, LaTex file. Revised manuscript. Additional minor revisions