Spinning waveforms in cubic effective field theories of gravity
Andreas Brandhuber, Graham R. Brown, Gang Chen, Gabriele Travaglini, Pablo Vives Matasan
Abstract
A bstract 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 Ĩ 1 and $$ {\overset{\sim }{G}}_3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>G</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mn>3</mml:mn> </mml:msub> </mml:math> . 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 $$ {\overset{\sim }{G}}_3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>G</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mn>3</mml:mn> </mml:msub> </mml:math> 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 Ĩ 1 similar shifts occur, but are accompanied by additional contributions that cannot be captured by simply shifting the scalar I 1 and Ĩ 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.