From amplitudes to gravitational radiation with cubic interactions and tidal effects

Abstract

We study the effect of cubic and tidal interactions on the spectrum of gravitational waves emitted in the inspiral phase of the merger of two non-spinning objects. There are two independent parity-even cubic interaction terms, which we take to be $I_1 = {R^{αβ}}_{μν} {R^{μν}}_{ρσ} {R^{ρσ}}_{αβ}$ and $G_3 = I_1-2 R^α\,_μ\,^β\,_ν R^μ\,_ρ\,^ν\,_σ R^ρ\,_α\,^σ\,_β$. The latter has vanishing pure graviton amplitudes but modifies mixed scalar/graviton amplitudes which are crucial for our study. Working in an effective field theory set-up, we compute the modifications to the quadrupole moment due to $I_1$, $G_3$ and tidal interactions, from which we obtain the power of gravitational waves radiated in the process to first order in the perturbations and leading order in the post-Minkowskian expansion. The $I_1$ predictions are novel, and we find that our results for $G_3$ are related to the known quadrupole corrections arising from tidal perturbations, although the physical origin of the $G_3$ coupling is unrelated to the finite-size effects underlying tidal interactions. We show this by recomputing such tidal corrections and by presenting an explicit field redefinition. In the post-Newtonian expansion our results are complete at leading order, which for the gravitational-wave flux is 5PN for $G_3$ and tidal interactions, and 6PN for $I_1$. Finally, we compute the corresponding modifications to the waveforms.

Figures (2)

• Figure 1: The single diagram contributing to the radiation process with an insertion of the operators $\mathcal{O}=I_1,I_2$. All momenta are treated as outgoing and the radiated graviton is taken to be soft.
• Figure 2: The two diagrams contributing to the gravitational radiation, where $\mathcal{O}$ denotes any of the two tidal interactions in \ref{['tidal']}. An overall Riemann tensor of the radiated graviton is factored out, so that $\mathcal{A}^{\mathcal{O}}=\mathcal{A}^{\mathcal{O}}_{\mu \nu \rho \sigma}\overline{R}^{\mu \nu \rho \sigma}(k\to 0)$.