Radial Oscillations of the HESS J1731-347 Compact Object Imposing the Karmarkar Condition

We model the light HESS J1731-347 compact object (of known stellar mass and radius) within Einstein’s General Relativity, imposing the Karmarkar condition in gravity for anisotropic stars. The three free parameters of the analytic solution are determined by imposing the matching conditions at the surface of the star for objects of known stellar mass and radius. Finally, using well-established criteria, it is shown that the solution is compatible with all requirements for well-behaved and realistic solutions. Furthermore, we study the radial oscillation modes, and we compare them to the ones corresponding to an isotropic star modeled by the Tolman IV exact analytic solution obtained a long time ago. A comparison between the large frequency separations is made as well.