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

TL;DR

This paper computes the gravitational wave stress-energy tensor in various alternative gravity theories, finding that in many cases it reduces to Isaacson's tensor, which is essential for testing these theories with gravitational wave data.

Contribution

It provides a systematic method to calculate the gravitational wave stress-energy tensor in a broad class of alternative theories of gravity, highlighting when modifications occur or vanish.

Findings

In many theories, the stress-energy tensor reduces to Isaacson's form.

Corrections to Isaacson's tensor can dominate in some theories.

The results are crucial for testing gravity theories with gravitational wave observations.

Abstract

The inspiral of binary systems in vacuum is controlled by the stress-energy of gravitational radiation and any other propagating degrees of freedom. For gravitational waves, the dominant contribution is characterized by an effective stress-energy tensor at future null infinity. We employ perturbation theory and the short-wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. We find that 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 exemplify this phenomenon by first considering dynamical Chern-Simons modified gravity, which corrects the action via a scalar field and the contraction of the Riemann tensor and its dual. We then 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. The calculations presented in this paper are crucial to perform systematic tests of such modified gravity theories through the orbital decay of binary pulsars or through gravitational wave observations.