Stellar configurations in f(R) theories of gravity

TL;DR

This paper investigates stellar structures in f(R) gravity theories, showing that typical models conflict with Solar System tests and exploring conditions for compatible solutions, including the impact on the star's metric and external space-time.

Contribution

It provides analytical and numerical analysis of stellar configurations in f(R) gravity, highlighting issues with Solar System constraints and proposing conditions for viable models.

Findings

Standard f(R) models predict incompatible Solar System behavior.

Stellar solutions in f(R) theories often lead to non-Schwarzschild external metrics.

Regular stellar metrics at the center conflict with Solar System observational constraints.

Abstract

We study stellar configurations and the space-time around them in metric $f(R)$ theories of gravity. In particular, we focus on the polytropic model of the Sun in the $f(R)=R-\mu^4/R$ model. We show how the stellar configuration in the $f(R)$ theory can, by appropriate initial conditions, be selected to be equal to that described by the Lane-Emden -equation and how a simple scaling relation exists between the solutions. We also derive the correct solution analytically near the center of the star in $f(R)$ theory. Previous analytical and numerical results are confirmed, indicating that the space-time around the Sun is incompatible with Solar System constraints on the properties of gravity. Numerical work shows that stellar configurations, with a regular metric at the center, lead to $\gamma_{PPN}\simeq1/2$ outside the star ie. the Schwarzschild-de Sitter -space-time is not the correct vacuum solution for such configurations. Conversely, by selecting the Schwarzschild-de Sitter -metric as the outside solution, we find that the stellar configuration is unchanged but the metric is irregular at the center. The possibility of constructing a $f(R)$ theory compatible with the Solar System experiments and possible new constraints arising from the radius-mass -relation of stellar objects is discussed.