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

TL;DR

This paper presents a non-singular, horizonless static spherically symmetric solution in Einstein-scalar-tensor gravity with a scalar potential, which is regular everywhere and stable against matter addition, challenging traditional singularity concepts.

Contribution

It introduces a new non-singular solution in Einstein-scalar-tensor gravity that avoids black hole horizons and singularities, expanding understanding of possible spacetime geometries.

Findings

Solution is non-singular and horizonless for all real coordinates.

Weak energy condition is violated near the origin, suggesting quantum effects.

Solution remains stable when ordinary matter is added.

Abstract

A static spherically symmetric metric in Einstein-scalar-tensor gravity theory with a scalar field potential $V[\phi]$ 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 $\rho_\phi > 0$ fails to be satisfied for $r\lesssim 1.3r_S$ (where $r_S$ is the Schwarzschild radius) but the strong energy condition $\rho_\phi+3p_\phi > 0$ 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.