Improved effective-one-body Hamiltonian for spinning black-hole binaries

Abstract

Building on a recent paper in which we computed the canonical Hamiltonian of a spinning test particle in curved spacetime, at linear order in the particle's spin, we work out an improved effectiveone-body (EOB) Hamiltonian for spinning black-hole binaries. As in previous descriptions, we endow the effective particle not only with a mass µ, but also with a spin S * . Thus, the effective particle interacts with the effective Kerr background (having spin SKerr) through a geodesic-type interaction and an additional spin-dependent interaction proportional to S * . When expanded in post-Newtonian (PN) orders, the EOB Hamiltonian reproduces the leading order spin-spin coupling and the spin-orbit coupling through 2.5PN order, for any mass-ratio. Also, it reproduces all spinorbit couplings in the test-particle limit. Similarly to the test-particle limit case, when we restrict the EOB dynamics to spins aligned or antialigned with the orbital angular momentum, for which circular orbits exist, the EOB dynamics has several interesting features, such as the existence of an innermost stable circular orbit, a photon circular orbit, and a maximum in the orbital frequency during the plunge subsequent to the inspiral. These properties are crucial for reproducing the dynamics and gravitational-wave emission of spinning black-hole binaries, as calculated in numerical relativity simulations.

Binary Black Hole Mergers in the First Advanced LIGO Observing Run

“…We provide a detailed evaluation of the source properties and inferred parameters of GW150914, GW151226, and LVT151012. We use models of the waveform covering the inspiral, merger, and ringdown phases based on combining post-Newtonian (PN) theory [19][20][21][22][23][24], the effective-onebody (EOB) formalism [25][26][27][28][29], and numerical relativity simulations [30][31][32][33][34][35][36]. One model is restricted to spins aligned with the orbital angular momentum [8,9], while the other allows for nonaligned orientation of the spins, which can lead to precession of the orbital plane [37,38].…”

Tests of General Relativity with GW150914

“…The analytical inspiral-merger-ringdown (IMR) waveform models used in this Letter were developed within two frameworks: (i) the effective-one-body (EOB) formalism [20][21][22][23][24], which combines PN results [10] with NR [25][26][27] and perturbation theory [28][29][30], and (ii) a phenomenological approach [31][32][33][34] based on extending frequencydomain PN expressions and hybridizing PN and EOB with NR waveforms. Specifically, here we adopt the doublespin, nonprecessing waveform model developed in Ref.…”

Sources of Gravitational Waves: Theory and Observations

“…The EOB conservative dynamics and waveforms have been extended to spinning BHs in [271,[286][287][288][289][290][291] and [292], respectively. In particular, motivated by the construction of a EOB Hamiltonian for spinning systems, that reduces to the Hamiltonian of a spinning particle in the extreme-mass ratio limit, [287] worked out, for the first time, the Hamiltonian of a spinning particle in curved spacetime at all orders in PN theory and linear in the particle's spin.…”