Short Distance Repulsive Gravity as a Consequence of Non Trivial PPN Parameters $\beta$ and $\gamma$

TL;DR

This paper explores a graviton-dilaton theory predicting non-trivial PPN parameters, resulting in repulsive gravity near compact objects and implications against black hole formation.

Contribution

It introduces a model-independent framework showing how specific dilaton potentials lead to repulsive gravity and absence of horizons for neutral stars.

Findings

Repulsive gravity occurs near the Schwarzschild radius.

No horizons form for charge neutral point stars.

Black hole formation is unlikely in this theory.

Abstract

We look for a graviton-dilaton theory which can predict non trivial values of the PPN parameters $\beta$ and/or $\gamma$ for a charge neutral point star, without any naked singularity. With the potential for dilaton $\phi$ set to zero, it contains one arbitrary function $\psi(\phi)$. Our requirements impose certain constraints on $\psi$, which lead to the following generic and model independent novel results: For a charge neutral point star, the gravitational force becomes repulsive at distances of the order of, but greater than, the Schwarzschild radius $r_0$. There is also no horizon for $r > r_0$. These results suggest that black holes are unlikely to form in a stellar collapse in this theory.