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

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.