Gravitational waves in Einstein-aether theory.

We study gravitational waves produced by N-body systems in Einstein-aether theory. In particular, we calculate the gravitational waveforms, polarizations, response functions of the detectors and the radiation power by using the post-Newtonian approximations to the lowest order. Applying the general formulas to three different triple systems with periodic orbits, we find that the scalar mode and the longitudinal mode (hb and hL) are all suppressed by a factor of c14 < O(10−5) with respect to the transverse-traceless modes (h+ and h×), while the vector modes (hX and hY ) are suppressed by a factor of c13 < O(10−15). We also find that gravitational waves depend sensitively on the configurations of the triple systems, their orientations with respect to the detectors, and the binding energies of the three compact bodies. The result for the first relativistic triple system, PSR J0337+1715, shows that the quadrupole emissions in different theories of gravity have almost the same amplitude, but the dipole emission can be as big as the quadrupole emission in Einstein-aether theory. This provides a very promising window to obtain severe constraints on Einstein-aether theory by multi-band gravitational wave astronomy.