The interior spacetimes of stars in Palatini f(R) gravity

TL;DR

This paper investigates the interior structure of stars within Palatini f(R) gravity, deriving modified stellar equations and analyzing how these differ from General Relativity, with implications for astrophysical observations.

Contribution

It derives a generalized TOV and mass equation for stars in Palatini f(R) gravity and explores the matching conditions with exterior solutions, highlighting differences from GR.

Findings

Modified mass-density relation in Palatini f(R) gravity

Negligible deviations for certain f(R) models

Consistency with Solar System and stellar constraints

Abstract

We study the interior spacetimes of stars in the Palatini formalism of f(R) gravity and derive a generalized Tolman-Oppenheimer-Volkoff and mass equation for a static, spherically symmetric star. We show that matching the interior solution with the exterior Schwarzschild-De Sitter solution in general gives a relation between the gravitational mass and the density profile of a star, which is different from the one in General Relativity. These modifications become neglible in models for which $\delta F(R) \equiv \partial f/\partial R - 1$ is a decreasing function of R however. As a result, both Solar System constraints and stellar dynamics are perfectly consistent with $f(R) = R - \mu^4/R$.