Effective Gravitational Wave Stress-energy Tensor in Alternative Theories of Gravity

The inspiral of binary systems in vacuum is controlled by the rate of change of the system's energy and angular momentum. In alternative theories, such a change is induced by the effective stress-energy carried away by gravitational radiation and any other propagating degrees of freedom. We employ perturbation theory and the short- wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. This tensor is generally a modification of that first computed by Isaacson, where the corrections can dominate over the general relativistic term. In a wide class of theories, however, these corrections identically vanish at asymptotically flat, future, null infinity, reducing the stress-energy tensor to Isaacson's. We consider a wide class of theories with dynamical scalar fields coupled to higher-order curvature invariants, and show that the gravitational wave stress-energy tensor still reduces to Isaacson's.