The gravitational wave stressenergy (pseudo)tensor in modified gravity
Abstract
The recent detections of gravitational waves by the advanced LIGO and Virgo detectors open up new tests of modified gravity theories in the strongfield and dynamical, extreme gravity regime. Such tests rely sensitively on the phase evolution of the gravitational waves, which is controlled by the energymomentum carried by such waves out of the system. We here study four different methods for finding the gravitational wave stressenergy pseudotensor in gravity theories with any combination of scalar, vector, or tensor degrees of freedom. These methods rely on the second variation of the action under shortwavelength averaging, the second perturbation of the field equations in the shortwavelength approximation, the construction of an energy complex leading to a LandauLifshitz tensor, and the use of Noether’s theorem in field theories about a flat background. We apply these methods in general relativity, JordanFierzBransDicky theoy, and EinsteinÆther theory to find the gravitational wave stressenergy pseudotensor and calculate the rate at which energy and linear momentum is carried away from the system. The stressenergy tensor and the rate of linear momentum loss in EinsteinÆther theory are presented here for the first time. We find that all methods yield the same rate of energy loss, although the stressenergy pseudotensor can be functionally different. We also find that the Noether method yields a stressenergy tensor that is not symmetric or gaugeinvariant, and symmetrization via the Belinfante procedure does not fix these problems because this procedure relies on Lorentz invariance, which is spontaneously broken in EinsteinÆther theory. The methods and results found here will be useful for the calculation of predictions in modified gravity theories that can then be contrasted with observations.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 March 2018
 DOI:
 10.1088/13616382/aaa7de
 arXiv:
 arXiv:1710.08863
 Bibcode:
 2018CQGra..35e5011S
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 18 pages, no figures, submitted to Class. and Quant. Gravity