The Gravitational Wave Stress-Energy (pseudo)-Tensor in Modified Gravity

Understand

The recent detections of gravitational waves by the advanced LIGO and Virgo detectors open up new tests of modified gravity theories in the strong-field and dynamical, extreme gravity regime.

• Such tests rely sensitively on the phase evolution of the gravitational waves, which is controlled by the energy-momentum carried by such waves out of the system.
• We here study four different methods for finding the gravitational wave stress-energy pseudo-tensor 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 short-wavelength averaging, the second perturbation of the field equations in the short-wavelength approximation, the construction of an energy complex leading to a Landau-Lifshitz tensor, and the use of Noether's theorem in field theories about a flat background.