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

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