# Bootstrapped Newtonian stars and black holes

## TL;DR

This paper explores equilibrium configurations of matter in a modified gravity model that includes self-interaction, revealing differences from general relativity such as the absence of a Buchdahl limit and potential for arbitrarily compact stars.

## Contribution

It introduces a bootstrapped Newtonian framework for stars and black holes, extending classical gravity with self-interaction terms and analyzing their equilibrium states.

## Key findings

- No Buchdahl limit in the model, allowing arbitrarily large compactness.
- Existence of a minimum compactness where escape velocity equals light speed.
- Potential to describe black hole interiors and deviations from GR in strong fields.

## Abstract

We study equilibrium configurations of a homogenous ball of matter in a bootstrapped description of gravity which includes a gravitational self-interaction term beyond the Newtonian coupling. Both matter density and pressure are accounted for as sources of the gravitational potential for test particles. Unlike the general relativistic case, no Buchdahl limit is found and the pressure can in principle support a star of arbitrarily large compactness. By defining the horizon as the location where the escape velocity of test particles equals the speed of light, like in Newtonian gravity, we find a minimum value of the compactness for which this occurs. The solutions for the gravitational potential here found could effectively describe the interior of macroscopic black holes in the quantum theory, as well as predict consequent deviations from general relativity in the strong field regime of very compact objects.