Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance

Abstract

The fulfillment of the space-asymptotic Poincaré algebra is used to derive new higher-order-in-spin interaction Hamiltonians for binary black holes in the Arnowitt-Deser-Misner canonical formalism almost completing the set of the formally 1/c 4 spin-interaction Hamiltonians involving nonlinear spin terms. To linear order in G, the expressions for the S 3 p and the S 2 p 2 Hamiltonians are completed. It is also shown that there are no quartic nonlinear S 4 Hamiltonians to linear order in G.

Spin-squared Hamiltonian of next-to-leading order gravitational interaction

“…The up to now missing NLO Hamiltonian H NLO S 2 1 finally results from the quadratic-in-spin static source terms derived in the last section, the nonstatic part of the Hamiltonian from [6] and the static linear-in-spin source term of the momentum constraint from [4]. As already noted in [4], the momentum constraint source term linear in spin gives a contribution via …”

“…Various contributions to the binary black hole (BBH) spin interaction Hamiltonian, even beyond quadratic order in spin, were derived in [5] by matching possible static source terms of the field constraints to the Kerr metric. In [6] various Hamiltonians, again also beyond quadratic order in spin, were calculated by inspecting the (global) Poincaré algebra. Astonishingly the momentum dependent part of the NLO spin(1)-spin(1), or S However, the Poincaré algebra leaves the static NLO S 2 1 part of the Hamiltonian completely unfixed.…”

Global symplectic structure-preserving integrators for spinning compact binaries

“…It has been developed by numerous authors (for references, see [62][63][64][65]67]). In the currently known conservative binary Hamiltonians for spinning black holes, the pure orbital or spinless parts and the spin effects are taken up to 3 PN order and 4 PN order, respectively [62][63][64][65]. For simplicity, here we consider only the orbital contributions and the spin effects up to 2 PN order.…”

“…Third, it is very good that the spin-orbit and spin-spin contributions can be solved exactly, but not everyone can have such good luck when various higherorder spin effects are included. In fact, the high-order spin effects given in [62][63][64][65] become too complicated. Therefore, a universal method for solving the spin Hamiltonian flows is merely a numerical integrator.…”

Periastron advance in spinning black hole binaries: Gravitational self-force from numerical relativity

“…[12] we explicitly write down the PN expression of the periastron advance for circular orbits, including all spin-independent, spin-orbit (SO), and spin-spin (SS) contributions up to 3.5PN order included. Higher-order interactions in the spins [47,48] will be neglected; hence we do not include the leadingorder 3.5PN terms cubic in the spins. We restrict to the conservative part of the dynamics, neglecting the dissipative effects related to gravitational-wave emission.…”