Binary mergers in bootstrapped Newtonian gravity: mass gap and black hole area law

TL;DR

This paper explores binary mergers within bootstrapped Newtonian gravity, revealing how higher-order couplings influence mass interpretation, black hole entropy, and gravitational wave signals, challenging traditional views on the mass gap and black hole area law.

Contribution

It introduces a modified Newtonian framework with higher-order couplings, providing new insights into black hole mergers, mass interpretation, and entropy in a non-relativistic context.

Findings

LIGO signals can be explained without violating the mass gap.

Black hole entropy follows a generalized area law.

Non-linear effects modify gravitational strength via Newton's constant.

Abstract

We study binary mergers in bootstrapped Newtonian gravity, where higher-order couplings are added to the non-relativistic Lagrangian for the Newtonian potential. In this theory, the Arnowitt-Deser-Misner (ADM) mass differs from both the proper mass of Newtonian gravity and the proper mass of general relativity, which affects the interpretation of astrophysical and cosmological events. The aforementioned difference particularly provides important phenomenological constraints for the mass of the emitted matter and the compactness of the final object after the merger. The interpretation of the GW150914 signal in this theory also shows that LIGO's findings do not violate the mass gap, contrary to usual claims. We indeed find that typical stellar black hole masses can fit LIGO's data for a considerable range of compactness values. We calculate the black hole entropy in this context, which leads to a generalised black hole area law. Non-linear effects are found to effectively change only the gravitational strength via the renormalization of Newton's constant in this case.