Critical compactness bound of a class of compact stars

TL;DR

This paper establishes an upper limit on the compactness of certain relativistic stars using a generalized Tolman VII solution, highlighting how matter distribution inhomogeneity influences stellar stability.

Contribution

It introduces a critical compactness bound for a class of compact stars based on a generalized Tolman VII solution, linking inhomogeneity and stability.

Findings

Derived an upper bound on star compactness ($M/R$) for stability.

Showed the influence of matter inhomogeneity on stellar stability.

Provided insights into the role of model parameters in star structure.

Abstract

Tolman VII solution [Phys. Rev. 55 (4), 364 (1939)] is an exact analytic solution to the Einstein field equations describing the space-time of a static spherically symmetric distribution of matter. The solution has been shown to be capable of describing the interior of compact objects like neutron stars. Generalized [Phys. Rev. D 92(12), 124005 (2015)] and modified [Phys. Rev. D 99(12), 124029 (2019)] versions of the solution are also available in the literature, which have been subsequently developed to accommodate a wide range of neutron star EOS. The stability of the modified Tolman VII solution has recently been analyzed by Posada et al [Phys. Rev. D 103(10), 104067 (2021)], which provides a critical value of the adiabatic index above which the stellar configuration becomes unstable against radial oscillations. In this paper, making use of the generalized version of the Tolman VII solution, we prescribe an upper bound on the compactness ($M/R$) beyond which the star becomes unstable against radial oscillations. Our study brings to attention the role of model parameters in the generalized Tolman VII solution. The analysis also provides new insight into the role of inhomogeneity of the matter distribution vis-a-vis equation of state (EOS) on the compactness of a relativistic star.