An Eccentric Binary Blackhole in Post-Newtonian Theory

Chowdhury, Sourav Roy; Khlopov, Maxim Yu.

doi:10.3390/sym14030510

Cited by 4 publications

(2 citation statements)

References 67 publications

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“…They investigated the influence of higher modes on the waveforms and developed a model that incorporates eccentricity and accurately describes the inspiral, merger, and ringdown phases. Chowdhury and Khlopov [14] studied an eccentric binary black hole system within the framework of post-Newtonian theory. Their research aimed to understand the behavior of binary black holes with non-circular orbits, providing insights into the dynamics and gravitational wave emissions of eccentric binary systems.…”

Section: Introductionmentioning

confidence: 99%

Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian

et al. 2023

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The equations of motion for a Lagrangian mainly refer to the acceleration equations, which can be obtained by the Euler–Lagrange equations. In the post-Newtonian Lagrangian form of general relativity, the Lagrangian systems can only maintain a certain post-Newtonian order and are incoherent Lagrangians since the higher-order terms are omitted. This truncation can cause some changes in the constant of motion. However, in celestial mechanics, Hamiltonians are more commonly used than Lagrangians. The conversion from Lagrangianto Hamiltonian can be achieved through the Legendre transformation. The coordinate momentum separable Hamiltonian can be computed by the symplectic algorithm, whereas the inseparable Hamiltonian can be used to compute the evolution of motion by the phase-space expansion method. Our recent work involves the design of a multi-factor correction map for the phase-space expansion method, known as the correction map method. In this paper, we compare the performance of the implicit algorithm in post-Newtonian Lagrangians and the correction map method in post-Newtonian Hamiltonians. Specifically, we investigate the extent to which both methods can uphold invariance of the motion’s constants, such as energy conservation and angular momentum preservation. Ultimately, the results of numerical simulations demonstrate the superior performance of the correction map method, particularly with respect to angular momentum conservation.

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Section: Introductionmentioning

confidence: 99%

Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian

et al. 2023

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“…The accurate computation of the gravitational waves (GW) from eccentric compact binary mergers has recently prompted a vibrant activity by the analytical and numerical relativity community [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. A main goal of this programme is to provide GW templates for binaries on generic orbits to be used in the next scientific observational runs of the LIGO-Virgo-Kagra (LVK) collaboration [19][20][21] and in the future LISA observations [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

New Avenue for Accurate Analytical Waveforms and Fluxes for Eccentric Compact Binaries

Albanesi,

Placidi,

Nagar

et al. 2022

Preprint

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We introduce a new paradigm for constructing accurate analytic waveforms (and fluxes) for eccentric compact binaries. Our recipe builds on the standard Post-Newtonian (PN) approach but (i) retains implicit time-derivatives of the phase space variables in the instantaneous part of the noncircular waveform, and then (ii) suitably factorizes and resums this partly PN-implicit waveform using effective-one-body (EOB) procedures. We test our prescription against the exact results obtained by solving the Teukolsky equation with a test-mass source orbiting a Kerr black hole, and compare the use of the exact vs PN equations of motion for the time derivatives computation. Focusing only on the quadrupole contribution, we find that the use of the exact equations of motion yields an analytical/numerical agreement of the (averaged) angular momentum fluxes that is improved by at least 45% with respect to previous work, with 4% fractional difference for eccentricity e = 0.9 and black hole dimensionless spin −0.9 ≤ â ≤ +0.9. We also find a remarkable convergence trend between Newtonian, 1PN and 2PN results. Our approach carries over to the comparable mass case using the resummed EOB equations of motion and paves the way to faithful EOB-based waveform model for long-inspiral eccentric binaries for current and future gravitational wave detectors.

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New avenue for accurate analytical waveforms and fluxes for eccentric compact binaries

et al. 2022

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An Eccentric Binary Blackhole in Post-Newtonian Theory

Cited by 4 publications

References 67 publications

Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian

Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian

New Avenue for Accurate Analytical Waveforms and Fluxes for Eccentric Compact Binaries

New avenue for accurate analytical waveforms and fluxes for eccentric compact binaries

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