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

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.

Comments: v1: 4 pages; v2: 5 pages, 1 table. Compared to the algorithm for constructing solution of the TOV equations in the anisotropic case in Phys. Rev. D \textbf{97} (2018) 124057, a new algorithm is proposed which leads to the regularly behaved physical quantities in the interior of a compact star; v3: matches the published version