Journal Article

PUBDB-2025-00770

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Action-angle variables of a binary black-hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order

Tanay, S. (Corresponding author) ; Cho, G.DESY* ; Stein, L. C.

2023
American Physical Society Ridge, NY

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Please use a persistent id in citations: doi:10.1103/PhysRevD.107.103040  doi:10.3204/PUBDB-2025-00770

Report No.: arXiv:2110.15351

Abstract: Accurate and efficient modeling of the dynamics of binary black holes (BBHs) is crucial to their detection through gravitational waves (GWs), with LIGO/Virgo/KAGRA, and LISA in the future. Solving the dynamics of a BBH system with arbitrary parameters without simplifications (like orbit- or precession-averaging) in closed-form is one of the most challenging problems for the GW community. One potential approach is using canonical perturbation theory which constructs perturbed action-angle variables from the unperturbed ones of an integrable Hamiltonian system. Having action-angle variables of the integrable 1.5 post-Newtonian (PN) BBH system is therefore imperative. In this paper, we continue the work initiated by two of us in arXiv:2012.06586, where we presented four out of five actions of a BBH system with arbitrary eccentricity, masses, and spins, at 1.5PN order. Here we compute the remaining fifth action using a novel method of extending the phase space by introducing unmeasurable phase space coordinates. We detail how to compute all the frequencies, and sketch how to explicitly transform to angle variables, which analytically solves the dynamics at 1.5PN. This lays the groundwork to analytically solve the conservative dynamics of the BBH system with arbitrary masses, spins, and eccentricity, at higher PN order, by using canonical perturbation theory.

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Contributing Institute(s):

1. Theoretische Astroteilchenphysik (Z_THAT)

Research Program(s):

1. 613 - Matter and Radiation from the Universe (POF4-613) (POF4-613)
2. LHCtoLISA - Precision Gravity: From the LHC to LISA (817791) (817791)

Experiment(s):

1. No specific instrument

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Electronics and Telecommunications Collection ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF >= 5 ; JCR ; SCOAP3 sponsored Journal ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Tanay, S. ; Cho, G.DESY* ; Stein, L. C. (Corresponding author)
Action-angle variables of a binary black-hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order
[10.3204/PUBDB-2022-00706]     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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