New effective-one-body Hamiltonian with next-to-leading order spin-spin coupling

Abstract

We present a new effective-one-body (EOB) Hamiltonian with next-to-leading order (NLO) spinspin coupling for black hole binaries endowed with arbitrarily oriented spins. The Hamiltonian is based on the model for parallel spins and equatorial orbits developed in [Physical Review D 90, 044018 (2014)], but differs from it in several ways. In particular, the NLO spin-spin coupling is not incorporated by a redefinition of the centrifugal radius rc, but by separately modifying certain sectors of the Hamiltonian, which are identified according to their dependence on the momentum vector. The gauge-fixing procedure we follow allows us to reduce the 25 different terms of the NLO spin-spin Hamiltonian in Arnowitt-Deser-Misner coordinates to only 9 EOB terms. This is an improvement with respect to the EOB model recently proposed in [Physical Review D 91, 064011 (2015)], where 12 EOB terms were involved. Another important advantage is the remarkably simple momentum structure of the spin-spin terms in the effective Hamiltonian, which is simply quadratic up to an overall square root. Moreover, a Damour-Jaranowski-Schäfer-type gauge could be established, thus allowing one to concentrate, in the case of circular and equatorial orbits, the whole spin-spin interaction in a single radial potential.

A new route towards merging massive black holes

“…The emitted frequencies during in-spiral are expected to peak approximately at the innermost stable circular orbit (ISCO) before the plunge-in phase and the actual merging. However, even determining the ISCO for a merging binary system is non-trivial and depends, for example, on the spins of the BHs (Balmelli & Damour 2015). This requires numerical or sophisticated (semi-)analytical calculations within general relativity and cannot simply be estimated using a test particle in a Kerr field.…”

Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings

“…test body relative to the background and the total centerof-mass-frame energy of the two-body system, which can be seen to arise from simple special-relativistic kinematics applied to scattering states at infinity. This turned out to be the same as (and gave new insight into) the energy map at the core of effective-one-body (EOB) models for relativistic binary dynamics [33][34][35][36][37][38][39][40][41]. Such EOB models, premised on modeling arbitrary-mass-ratio two-body motion after test-body motion in a fixed background while also incorporating information from PN and selfforce calculations and numerical relativity simulations, have played an important role in the detection and analysis of (including tests of general relativity with) the first gravitational wave signals [1][2][3][4][42][43][44].…”

Time-domain effective-one-body gravitational waveforms for coalescing compact binaries with nonprecessing spins, tides, and self-spin effects

“…Next-to-leading order spin-spin effects can be incorporated in a different fashion depending on whether the spins are generic or aligned with the orbital angular momentum. This is still ongoing work that needs further investigation [103]. In the case of two NSs the recipe we propose here to include spin-spin couplings at LO is just to replace the definition of the effective spinâ 0 in 10 Since the spin magnitude of each NS composing the binary is expected to be small (χ 0.1), we may a priori expect this order of approximation to be sufficient, although the corresponding Hamiltonian at NLO has been obtained recently with different approaches [102].…”