Spinning waveforms in cubic effective field theories of gravity

TL;DR

This paper derives comprehensive all-order-in-spin gravitational waveforms for scattering Kerr black holes with cubic gravity modifications, employing three methods and revealing shifts akin to Newman-Janis transformations.

Contribution

It provides the first analytic all-order-in-spin waveforms in cubic gravity theories for Kerr black hole scattering, including parity-even and parity-odd interactions, using three independent computational approaches.

Findings

Waveforms expressed in terms of shifted scalar waveforms for certain deformations.

Absence of leading-order corrections to gravitational memory.

Comparison of three computational methods for efficiency and compactness.

Abstract

We derive analytic all-order-in-spin expressions for the leading-order time-domain waveforms generated in the scattering of two Kerr black holes with arbitrary masses and spin vectors in the presence of all independent cubic deformations of Einstein-Hilbert gravity. These are the two parity-even interactions $I_1$ and $G_3$, and the parity-odd ones $\tilde{I}_1$ and $\tilde{G}_3$. Our results are obtained using three independent methods: a particularly efficient direct integration and tensor reduction approach; integration by parts combined with the method of differential equations; and finally a residue computation. For the case of the $G_3$ and $\tilde{G}_3$ deformations we can express the spinning waveform in terms of the scalar waveform with appropriately shifted impact parameters, which are reminiscent of Newman-Janis shifts. For $I_1$ and $\tilde{I}_1$ similar shifts occur, but are accompanied by additional contributions that cannot be captured by simply shifting the scalar $I_1$ and $\tilde{I}_1$ waveforms. We also show the absence of leading-order corrections to gravitational memory. Our analytic results are notably compact, and we compare the effectiveness of the three methods used to obtain them. We also briefly comment on the magnitude of the corrections to observables due to cubic deformations.