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

J. W. Moffat
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Abstract

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

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J. W. Moffat. 2008-06-11. Non-Singular Spherically Symmetric Solution in Einstein-Scalar-Tensor Gravity. https://arxiv.org/abs/gr-qc/0702070

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