Universality in static spherically symmetric solutions of f(R) gravity

TL;DR

This paper investigates static spherically symmetric vacuum solutions in f(R) gravity, revealing universal behaviors of the scalaron field and metric parameters across different models and configurations, especially for astrophysically relevant masses.

Contribution

It provides analytical and numerical analysis of SSS solutions in f(R) gravity, highlighting universal properties and behaviors of the scalaron field and metric parameters across various models.

Findings

Scalaron field exhibits universal behavior regardless of configuration mass.

Solutions show similar properties for different scalaron masses and sizes of scalarization region.

Asymptotic metric parameters near the naked singularity are characterized for all models.

Abstract

f(R) gravity is a well-known modification of General Relativity, that can be reduced to a scalar-tensor theory by a conformal transformation (Einstein frame). We study static spherically symmetric (SSS) asymptotically flat vacuum configurations of the f(R) gravity in the Einstein frame for three known scalaron potentials. The main attention is paid to solutions in case of astrophysically relevant configuration masses and scalaron mass $\mu$ larger than several meV. Analytical and numerical analysis reveals remarkably similar properties of some elements of the SSS solutions for different M, $\mu$ and sizes of the scalarization region $r_0$. In particular, the scalaron field has universal behavior regardless of the configurations mass and $r_0>100 r_g$ in case of each of the models considered. Moreover, some elements of the solutions are practically the same for the different models. Asymptotic parameters of the metric near the naked singularity at the center of the SSS configuration are obtained for all the models.