Effective metric outside bootstrapped Newtonian sources

TL;DR

This paper derives a full space-time metric from a bootstrapped Newtonian potential for static, spherically symmetric sources, showing it closely resembles Schwarzschild but with a larger size for the same mass.

Contribution

It provides a method to reconstruct the space-time metric from a Newtonian potential and explores its properties within experimental bounds.

Findings

Reconstructed metric is close to Schwarzschild outside the horizon.

The metric predicts a larger size for the same mass compared to Schwarzschild.

Post-Newtonian parameters can constrain the underlying theory.

Abstract

We determine the complete space-time metric from the bootstrapped Newtonian potential generated by a static spherically symmetric source in the surrounding vacuum. This metric contains post-Newtonian parameters which can be further used to constrain the complete underlying dynamical theory. For values of the post-Newtonian parameters within experimental bounds, the reconstructed metric appears very close to the Schwarzschild solution of General Relativity in the whole region outside the event horizon. The latter is however larger in size for the same value of the mass compared to the Schwarzschild case.