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

Rickmoy Samanta, Sashwat Tanay, Leo C. Stein

Research output: Contribution to journalArticlepeer-review

Abstract

The closed-form solution of the 1.5 post-Newtonian (PN) accurate binary black hole (BBH) Hamiltonian system has proven to be evasive for a long time since the introduction of the system in 1966. Solutions of the PN BBH systems with arbitrary parameters (masses, spins, eccentricity) are required for modeling the gravitational waves emitted by them. Accurate models of gravitational waves are crucial for their detection by LIGO/Virgo and LISA. Only recently, two solution methods for solving the BBH dynamics were proposed in Ref. [G. Cho and H. M. Lee, Phys. Rev. D 100, 044046 (2019)PRVDAQ2470-001010.1103/PhysRevD.100.044046] (without using action-angle variables), and Refs. [S. Tanay, Phys. Rev. D 103, 064066 (2021)PRVDAQ2470-001010.1103/PhysRevD.103.064066, S. Tanay, Phys. Rev. D 107, 103040 (2023)PRVDAQ2470-001010.1103/PhysRevD.107.103040] (action-angle based). This paper combines the ideas laid out in the above articles, fills the missing gaps and compiles 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 the result of numerical integration of the evolution equations. The level of agreement between these solutions provides a numerical verification for all the five action variables constructed in Refs. [S. Tanay, Phys. Rev. D 103, 064066 (2021)PRVDAQ2470-001010.1103/PhysRevD.103.064066, S. Tanay, Phys. Rev. D 107, 103040 (2023)PRVDAQ2470-001010.1103/PhysRevD.107.103040]. This paper hence serves as a stepping stone for pushing the action-angle-based solution to 2PN order via canonical perturbation theory.

Original languageEnglish
Article number124039
JournalPhysical Review D
Volume108
Issue number12
DOIs
StatePublished - 15 Dec 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 American Physical Society.

Funding

S. T. thanks Nicolás Yunes for an invitation to conduct a lecture workshop at the University of Illinois Urbana-Champaign. The workshop served as the initial impetus for this project. We also thank Nathan Johnson-McDaniel for providing useful suggestions, and José T. Gálvez Ghersi for a careful reading of this manuscript. S. T. was partially supported by PSL postdoctoral fellowship. The work of L. C. S. was partially supported by NSF CAREER Award No. PHY-2047382. R. S. acknowledges support from DST India (Grant No. IFA19-PH231).

FundersFunder number
DST IndiaIFA19-PH231
National Science FoundationPHY-2047382
Université de Recherche Paris Sciences et Lettres

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