Abstract
It has been suggested that amplitudes for quantum higher-spin massive particles exchanging gravitons lead, via a classical limit, to results for scattering of spinning black holes in general relativity, when the massive particles are in a certain way minimally coupled to gravity. Such limits of such amplitudes suggest, at least at lower orders in spin, up to second order in the gravitational constant $G$, that the classical aligned-spin scattering function for an arbitrary-mass-ratio two-spinning-black hole system can be obtained by a simple kinematical mapping from that for a spinning test black hole scattering off a stationary background Kerr black hole. Here we test these suggestions, at orders beyond the reach of the post-Newtonian and post-Minkowskian results used in their initial partial verifications, by confronting them with results from general-relativistic ``self-force'' calculations of the linear perturbations of a Kerr spacetime sourced by a small orbiting body, here considering only results for circular orbits in the equatorial plane. We translate between scattering and circular-orbit results by assuming the existence of a local-in-time canonical Hamiltonian governing the conservative dynamics of generic (bound and unbound) aligned-spin orbits, while employing the associated first law of spinning binary mechanics. To the extent possible with available self-force results, we confirm, through linear order in the mass ratio, some previous conjectures which would begin to fill in the spin-dependent parts of the conservative dynamics for arbitrary-mass-ratio aligned-spin binary black holes at the fourth-and-a-half and fifth post-Newtonian orders.
Highlights
The early successes of gravitational-wave astronomy have relied on highly accurate solutions to the binary black hole problem in general relativity (GR)
It has been suggested that amplitudes for quantum higher-spin massive particles exchanging gravitons lead, via a classical limit, to results for scattering of spinning black holes in general relativity, when the massive particles are in a certain way minimally coupled to gravity
Such limits of such amplitudes suggest, at least at lower orders in spin, up to second order in the gravitational constant G, that the classical alignedspin scattering function for an arbitrary-mass-ratio two-spinning-black hole system can be obtained by a simple kinematical mapping from that for a spinning test black hole scattering off a stationary background Kerr black hole
Summary
The early successes of gravitational-wave astronomy have relied on highly accurate solutions to the binary black hole problem in general relativity (GR) These have been obtained both from intensive numerical-relativity simulations (see e.g., [1]) and, with overlapping domains of validity, from high-order calculations in the weak-field– slow-motion post-Newtonian (PN) approximation [2,3], along with approaches to combining, interpolating and extrapolating these two crucial sources of information. While traditional classical methods had previously reached the second post-Minkowskian (2PM) level, i.e., through the second order in the gravitational constant G, notably including Westpfahl’s computation of the 2PM scatteringangle function for two monopolar “point masses” [27], a recent landmark has been the first calculation yielding analogous results at 3PM/two-loop order by Bern, et al [28,29], using amplitudes computed with on shell unitarity methods Whereas these results concern gravitational scattering of nonspinning bodies, our primary interest in this paper is in the dynamics of spinning bodies—spinning black holes (BHs)
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