Effective geometrostatics of spherical stars beyond general relativity

TL;DR

This paper develops general tools for analyzing spherical star equilibrium in modified gravity theories, deriving a universal TOV equation and exploring effects like black hole cores and limits on compactness.

Contribution

It introduces a general framework for stellar equilibrium in alternative gravity theories and derives a universal TOV equation compatible with these models.

Findings

Mitigation of the Buchdahl limit in modified gravity

Existence of regular black hole solutions with perfect fluid cores

Universal aspects of gravity weakening on stellar structures

Abstract

We provide a set of general tools to study the problem of stellar equilibrium in any gravitational theory in which spherically symmetric spacetimes satisfy master field equations taking the form of an equality between an identically conserved tensor, with derivatives of up to second order in the metric, and an identically conserved matter tensor. We derive the most general expression for the Tolman--Oppenheimer--Volkoff equation of stellar equilibrium that is compatible with these minimal requirements. A general discussion of the conditions that guarantee geodesic completeness at the center of symmetry is also presented. The equations of stellar equilibrium are integrated in a subset of the space of allowed deformations of general relativity proposed by Ziprick and Kunstatter, allowing us to illustrate universal aspects associated with the weakening of the strength of gravity, such as the mitigation of the Buchdahl limit obtained in general relativity or the existence of static solutions describing regular black holes with perfect fluid cores.