Slowly Rotating Anisotropic Neutron Stars with a Parametrized Equation of State

TL;DR

This paper investigates how anisotropy affects slowly rotating neutron stars by extending the Hartle-Thorne formalism, deriving universal relations, and testing them across various equations of state.

Contribution

It introduces a method to incorporate anisotropy into the Hartle-Thorne formalism and develops universal relations applicable to different equations of state.

Findings

Anisotropy increases the gravitational mass of rotating neutron stars by 12-25%.

Universal relations for moment of inertia, binding energy, and quadrupole moment are established.

Results are consistent with recent studies and validated across multiple equations of state.

Abstract

In this work, we study the impact of anisotropy on slowly rotating neutron stars by extending the Hartle-Thorne formalism in general relativity to include anisotropy in pressure up to second order in the angular velocity. We assess the presence of anisotropy within the star by employing a quasi-local relationship. Our results show that the ratio between the gravitational mass of the fastest anisotropic rotating configurations and the corresponding non-rotating ones ranges from $1.12$ to $1.25$, consistent with recent findings. We develop universal relations for the moment of inertia, binding energy, and quadrupole moment of the rotating stars. These relations are tested against various equations of state, which were modeled by a piecewise polytropic function with continuous sound speed.