Star equilibrium: from BNG to TOV

TL;DR

This paper explores how modifications inspired by the TOV equation affect equilibrium solutions in bootstrapped Newtonian gravity, comparing them with classical models and analyzing implications for stellar compactness and stability.

Contribution

It introduces TOV-inspired terms into BNG, providing new insights into stellar equilibrium and the absence of a Buchdahl limit in this framework.

Findings

BNG stars lack a Buchdahl limit regardless of added terms

Certain extra terms can induce negative pressure inside stars

Comparisons show differences between BNG, Newtonian, and GR solutions

Abstract

We study the role of the equilibrium equation in bootstrapped Newtonian gravity (BNG) by including terms inspired by the post-Newtonian expansion of the Tolman-Oppenheimer-Volkov (TOV) equation. We then compare (approximate) BNG solutions for homogenous stars with their Newtonian and General Relativistic exact solutions. Regardless of the additional terms from the conservation equation, BNG stars do not exhibit a Buchdahl limit. However, specific extra terms added to this equation can cause the pressure to become negative inside stars with compactness smaller than the critical values for BNG black hole formation.