Comment on "Covariant Tolman-Oppenheimer-Volkoff equations. II. The anisotropic case"

TL;DR

This paper critiques a previous method for modeling anisotropic compact stars using covariant TOV equations, identifies a singularity issue, and proposes a new scheme that produces physically regular solutions, demonstrated on strange quark star models.

Contribution

It introduces a new scheme for constructing physically regular anisotropic star models based on covariant TOV equations, overcoming previous singularity problems.

Findings

Previous method leads to singular anisotropic pressure at the star's center.

New scheme yields regular physical quantities inside the star.

Models of anisotropic strange quark stars are successfully constructed.

Abstract

Recently, the covariant formulation of the Tolman-Oppenheimer-Volkoff (TOV) equations for studying the equilibrium structure of a spherically symmetric compact star in the presence of the pressure anisotropy in the interior of a star was presented in Phys. Rev. D \textbf{97} (2018) 124057. It was suggested there that the anisotropic solution of these equations can be obtained by finding, first, the solution of the common TOV equations for the isotropic pressure, and then by solving the differential equation for the anisotropic pressure whose particular form was established on the basis of the covariant TOV equations. It turns out that the anisotropic pressure determined according to this scheme has a nonremovable singularity $\Pi\sim\frac{1}{r^2}$ in the center of a star, and, hence, the corresponding anisotropic solution cannot represent a physically relevant model of an anisotropic compact star. A new scheme for constructing the anisotropic solution, based on the covariant TOV equations, is suggested, which leads to the regularly behaved physical quantities in the interior of a star. A new algorithm is applied to build model anisotropic strange quark stars with the MIT bag model equation of state.