Moment of Inertia for Axisymmetric Neutron Stars in the Standard-Model Extension

TL;DR

This paper introduces a novel relativistic method to calculate the moment of inertia for axisymmetric neutron stars within the Lorentz-violating Standard-Model Extension framework, expanding the understanding of neutron star properties in alternative gravity theories.

Contribution

It presents the first relativistic calculation of neutron star moment of inertia in a Lorentz-violating gravity theory, using a numerical finite element approach.

Findings

Derived a PDE for neutron star rotation under Lorentz violation

Numerically computed the MOI for axisymmetric NSs in SME

Compared Lorentz-violating effects with Newtonian deformation results

Abstract

We develop a consistent approach to calculate the moment of inertia (MOI) for axisymmetric neutron stars (NSs) in the Lorentz-violating Standard-Model Extension (SME) framework. To our knowledge, this is the first relativistic MOI calculation for axisymmetric NSs in a Lorentz-violating gravity theory other than deformed, rotating NSs in the General Relativity. Under Lorentz violation, there is a specific direction in the spacetime and NSs get stretched or compressed along that direction. When a NS is spinning stationarily along this direction, a conserved angular momentum and the concept of MOI are well defined. In the SME framework, we calculate the partial differential equation governing the rotation and solve it numerically with the finite element method to get the MOI for axisymmetric NSs caused by Lorentz violation. Besides, we study an approximate case where the correction to the MOI is regarded solely from the deformation of the NS and compare it with its counterpart in the Newtonian gravity. Our formalism and the numerical method can be extended to other theories of gravity for static axisymmetric NSs.