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 nonrotating 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.