Gravitational wave in Lorentz violating gravity

TL;DR

This paper derives a linearized gravitational wave solution in Lorentz-violating gravity, revealing potential superluminal speeds while maintaining causality and conserved energy-momentum.

Contribution

It provides explicit plane-wave solutions and dispersion relations for gravitational waves in anisotropic, Lorentz-violating spacetime, a novel analysis in modified gravity theories.

Findings

Gravitational waves can travel faster than light in this framework.

Energy-momentum of gravitational waves remains well-defined and conserved.

Causality is preserved despite superluminal propagation.

Abstract

By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitational wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the casuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.