Slowly Rotating Anisotropic Neutron Stars in General Relativity and Scalar-Tensor Theory

TL;DR

This study investigates how anisotropy influences the properties of slowly rotating neutron stars within General Relativity and scalar-tensor theories, highlighting potential observational signatures in binary pulsar systems.

Contribution

It introduces the effects of anisotropy on rotating neutron stars in both theories and provides a criterion for the onset of scalarization based on anisotropic pressures.

Findings

Anisotropy significantly affects neutron star moment of inertia.

Scalarization effects are amplified or diminished depending on pressure anisotropy.

Binary pulsar data could constrain neutron star core anisotropy.

Abstract

Some models (such as the Skyrme model, a low-energy effective field theory for QCD) suggest that the high-density matter prevailing in neutron star interiors may be significantly anisotropic. Anisotropy is known to affect the bulk properties of nonrotating neutron stars in General Relativity. In this paper we study the effects of anisotropy on slowly rotating stars in General Relativity. We also consider one of the most popular extensions of Einstein's theory, namely scalar-tensor theories allowing for spontaneous scalarization (a phase transition similar to spontaneous magnetization in ferromagnetic materials). Anisotropy affects the moment of inertia of neutron stars (a quantity that could potentially be measured in binary pulsar systems) in both theories. We find that the effects of scalarization increase (decrease) when the tangential pressure is bigger (smaller) than the radial pressure, and we present a simple criterion to determine the onset of scalarization by linearizing the scalar-field equation. Our calculations suggest that binary pulsar observations may constrain the degree of anisotropy or even, more optimistically, provide evidence for anisotropy in neutron star cores.