Precession of Neutron Stars Under Lorentz Violation and Observational Consequences

The Standard-Model Extension is a framework that catalogs all Lorentz-violating field operators. We investigate the anisotropic correction to the Newtonian gravitational energy for spheroids in the minimal gravitational Standard-Model Extension and solve the rotation dynamics of spheroids. The forced-precession solution given by Nordtvedt in the parametrized post-Newtonian formalism is recovered and applied to constrain the coefficients for Lorentz violation with two solitary millisecond pulsars. The other solution describes an otherwise freely precessing star in the presence of Lorentz violation. The observational consequences on radio signals and continuous gravitational waves emitted by neutron stars are studied.