Neutron Star Structure in the Minimal Gravitational Standard-Model Extension and the Implication to Continuous Gravitational Waves

TL;DR

This paper explores how minimal Lorentz violation, within the Standard-Model Extension framework, affects neutron star structure and proposes a new method to test Lorentz invariance through continuous gravitational wave observations.

Contribution

It derives modified hydrostatic equations incorporating Lorentz violation and applies them to neutron stars, providing a novel approach to test Lorentz invariance in strong gravitational fields.

Findings

Derived modified TOV equations with Lorentz violation

Calculated neutron star quadrupole moments and gravitational radiation

Proposed a new test for Lorentz invariance using gravitational wave data

Abstract

Tiny violation of Lorentz invariance has been the subject of theoretic study and experimental test for a long time. We use the Standard-Model Extension (SME) framework to investigate the effect of the minimal Lorentz violation on the structure of a neutron star. A set of hydrostatic equations with modifications from Lorentz violation are derived, and then the modifications are isolated and added to the Tolman-Oppenheimer-Volkoff (TOV) equation as the leading-order Lorentz-violation corrections in relativistic systems. A perturbation solution to the leading-order modified TOV equations is found. The quadrupole moments due to the anisotropy in the structure of neutron stars are calculated and used to estimate the quadrupole radiation of a spinning neutron star with the same deformation. The calculation puts forward a new test for Lorentz invariance in the strong-field regime when continuous gravitational waves are observed in the future.