Closed-form solutions of spinning, eccentric binary black holes at 1.5 post-Newtonian order

Abstract

The closed-form solution of the 1.5 post-Newtonian (PN) accurate binary black hole (BBH) Hamiltonian system has proven to be difficult to obtain for a long time since its introduction in 1966. Closed-form solutions of the PN BBH systems with arbitrary parameters (masses, spins, eccentricity) are required for modeling the gravitational waves (GWs) emitted by them. Accurate models of GWs are crucial for their detection by LIGO/Virgo and LISA. Only recently, two solution methods for solving the BBH dynamics were proposed in arXiv:1908.02927 (without using action-angle variables), and arXiv:2012.06586, arXiv:2110.15351 (action-angle based). This paper combines the ideas laid out in the above articles, fills the missing gaps and provides the two solutions which are fully 1.5PN accurate. We also present a public Mathematica package BBHpnToolkit which implements these two solutions and compares them with a fully numerical treatment. The level of agreement between these solutions provides a numerical verification for all the five actions constructed in arXiv:2012.06586, and arXiv:2110.15351. This paper hence serves as a stepping stone for pushing the action-angle-based solution to 2PN order via canonical perturbation theory.

(2+15) pages, (1+4) figures. This version is composed of an erratum (wrt. the previous arXiv preprint version), and the fully revised article appended thereafter

References in corpus (17)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• Constructing Gravitational Waves from Generic Spin-Precessing Compact Binary Inspirals
• Multi-timescale analysis of phase transitions in precessing black-hole binaries
• An eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory
• Effective potentials and morphological transitions for binary black-hole spin precession
• Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction
• Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Fourier domain gravitational waveforms for precessing eccentric binaries
• Ready-to-use Fourier domain templates for compact binaries inspiraling along moderately eccentric orbits
• Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform
• Spin effects in the phasing of gravitational waves from binaries on eccentric orbits
• Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order
• Analytic Keplerian-type parametrization for general spinning compact binaries with the leading order spin-orbit interaction
• Action-angle variables of a binary black hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order

Cited by in corpus (1)

• Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order