Cylindrical gravitational waves in Einstein-Aether theory

Along the lines of the Einstein-Rosen wave equation of General Relativity (GR), we derive a gravitational wave equation with cylindrical symmetry in the Einstein-aether (EA) theory. We show that the gravitational wave in the EA is periodic in time for both the metric functions Psi(r, t) and H(r, t). However, in GR, Psi(r, t) is periodic in time, but H(r, t) is semi-periodic in time, having a secular drifting in the wave frequency. The evolution of wave pulses of a given width is entirely different in both theories in the H(r, t) metric function due to this frequency drifting. Another fundamental difference between the two theories is the gravitational wave velocity. While in GR, the waves propagate with the speed of light, in EA, there is no upper limit to the wave velocity, reaching infinity if c13 -> 1 and zero if c13 -> - infinity. We also show that energy-momentum pseudotensor and superpotential get contributions from aether in addition to the usual gravitational field part. All these characteristics are observational signatures that differentiate GR and EA that might aid in the search for new physics in the cosmological background of stochastic gravitational waves discovered recently by the Pulsar Timing Array collaborations such as NANOGrav, EPTA, PPTA, InPTA, and CPTA.