Radiation reaction for spinning bodies in effective field theory. I. Spin-orbit effects

Abstract

We compute the leading post-Newtonian (PN) contributions at linear order in the spin to the radiationreaction acceleration and spin evolution for binary systems, which enter at fourth PN order. The calculation is carried out, from first principles, using the effective field theory framework for spinning compact objects, in both the Newton-Wigner and covariant spin supplementary conditions. A nontrivial consistency check is performed on our results by showing that the energy loss induced by the resulting radiation-reaction force is equivalent to the total emitted power in the far zone, up to so-called "Schott terms." We also find that, at this order, the radiation reaction has no net effect on the evolution of the spins. The spin-spin contributions to radiation reaction are reported in a companion paper.

Radiation reaction for spinning bodies in effective field theory. II. Spin-spin effects

“…As we discussed in [4], following the in-in formalism [72,73], the nonconservative dynamics is described by an extended Routhian, whereas for the spin dynamics we have…”

“…From the Routhian [including the term in (2.4)] we can obtain the leading order spin-spin equations of motion in the conservative sector, both with OðS 1 S 2 Þ and OðS 2 a Þ terms, namely, the relative accelerations that enter at 2PN order, We will use these expressions in what follows in order to include spin-spin effects that contribute through derivatives of spin-independent multipole moments, just as we did in [4].…”

“…In a companion paper [4], we reported the resulting radiation-reaction equations of motion to linear order in the spins, which appear at fourth postNewtonian (4PN) order, using the effective field theory (EFT) formalism. At this order conservative contributions are also known using more traditional methods [5] as well as the EFT approach [6,7], encompassing spin-independent [8][9][10][11][12][13][14][15][16][17][18] (see also [19,20]) and spin-dependent terms.…”

“…However, we report-for the first time to our knowledge-the effects of backreaction due to the finite size of the spinning bodies, computed from first principles. 2 We perform a consistency check similar to the one presented in [4] that demonstrates the equivalence between the energy loss induced by the radiation-reaction acceleration and the total emitted power in the far zone, up to total time derivatives. Contrary to what occurs in the spin-orbit sector [4,71], we find that spin-spin effects in the radiation reaction do affect the evolution of the spin vectors, leading to a radiation-reaction induced contribution to the full precession equation consistent with the findings in [65], this time also including finite-size effects.…”

“…2 We perform a consistency check similar to the one presented in [4] that demonstrates the equivalence between the energy loss induced by the radiation-reaction acceleration and the total emitted power in the far zone, up to total time derivatives. Contrary to what occurs in the spin-orbit sector [4,71], we find that spin-spin effects in the radiation reaction do affect the evolution of the spin vectors, leading to a radiation-reaction induced contribution to the full precession equation consistent with the findings in [65], this time also including finite-size effects. Throughout this paper we use the same conventions as in [4], to which we also refer the reader for background discussion and references regarding details about some of the methods employed in this work.…”