Hydrostatic equilibrium and stellar structure in f(R)-gravity

TL;DR

This paper explores how f(R)-gravity modifies stellar hydrostatic equilibrium by deriving a new integro-differential Laé-Emden equation and analyzing its solutions, revealing compatibility with standard models in the Newtonian limit.

Contribution

It introduces a modified Laé-Emden equation from f(R)-gravity in the Newtonian limit and analyzes its solutions for stellar structures.

Findings

Modified equation reduces to standard Laé-Emden when f(R) approaches R.

Solutions for certain polytropic indices are obtained and analyzed.

Results are compatible with classical General Relativity solutions.

Abstract

We investigate the hydrostatic equilibrium of stellar structure by taking into account the modi- fied La\'e-Emden equation coming out from f(R)-gravity. Such an equation is obtained in metric approach by considering the Newtonian limit of f(R)-gravity, which gives rise to a modified Poisson equation, and then introducing a relation between pressure and density with polytropic index n. The modified equation results an integro-differential equation, which, in the limit f(R) \rightarrow R, becomes the standard La\'e-Emden equation. We find the radial profiles of gravitational potential by solving for some values of n. The comparison of solutions with those coming from General Relativity shows that they are compatible and physically relevant.