Noether's stars in $f(\cal {R})$ gravity

TL;DR

This paper uses Noether symmetry to derive solutions in $f({\cal R})$ gravity, enabling the modeling of neutron stars with properties that differ from those predicted by General Relativity, including more massive stable stars.

Contribution

It introduces a method to construct spherically symmetric solutions in $f({\cal R})$ gravity using Noether symmetries, linking conserved quantities to stellar properties.

Findings

Derived $M-R$ relations depending on Noether conserved quantities.

Showed the possibility of stable, more massive neutron stars in $f({\cal R})$ gravity.

Provided examples for power law $f({\cal R})$ models.

Abstract

The Noether Symmetry Approach can be used to construct spherically symmetric solutions in $f({\cal R})$ gravity. Specifically, the Noether conserved quantity is related to the gravitational mass and a gravitational radius that reduces to the Schwarzschild radius in the limit $f({\cal R})\rightarrow {\cal R}$. We show that it is possible to construct the $M-R$ relation for neutron stars depending on the Noether conserved quantity and the associated gravitational radius. This approach enables the recovery of extreme massive stars that could not be stable in the standard Tolman-Oppenheimer-Volkoff based on General Relativity. Examples are given for some power law $f({\cal R})$ gravity models.