Gravitational waves in Einstein-{\ae}ther and generalized TeVeS theory after GW170817

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In this work, we discuss the polarization contents of Einstein-\ae ther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field.

• We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom.
• We find the plane wave solutions are then found, and identify the polarizations by examining the geodesic deviation equations.
• We find that there are five polarizations in Einstein-\ae ther theory and six polarizations in the generalized TeVeS theory.