Close encounters of three black holes

Campanelli, Manuela; Lousto, Carlos O.; Zlochower, Yosef

doi:10.1103/physrevd.77.101501

Cited by 49 publications

(101 citation statements)

References 54 publications

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“…This triggered research on the numerical evolution of the full nonlinear Einstein equations in four [10][11][12][13][14][15][16][17][18] and higher dimensions [19][20][21][22][23]. The validation of numerical codes requires semianalytical tools, such as post-Newtonian theory, BH perturbation theory and zero-frequency expansions to model BH collisions.…”

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confidence: 99%

Radiation from particles with arbitrary energy falling into higher-dimensional black holes

2011

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We consider point particles with arbitrary energy per unit mass E that fall radially into a higherdimensional, nonrotating, asymptotically flat black hole. We compute the energy and linear momentum radiated in this process as functions of E and of the spacetime dimensionality D = n + 2 for n = 2, . . . , 9 (in some cases we go up to 11). We find that the total energy radiated increases with n for particles falling from rest (E = 1). For fixed particle energies 1 < E ≤ 2 we show explicitly that the radiation has a local minimum at some critical value of n, and then it increases with n. We conjecture that such a minimum exists also for higher particle energies. The present point-particle calculation breaks down when n = 11, because then the radiated energy becomes larger than the particle mass. Quite interestingly, for n = 11 the radiated energy predicted by our calculation would also violate Hawking's area bound. This hints at a qualitative change in gravitational radiation emission for n 11. Our results are in very good agreement with numerical simulations of low-energy, unequal-mass black hole collisions in D = 5 (that will be reported elsewhere) and they are a useful benchmark for future nonlinear evolutions of the higher-dimensional Einstein equations.

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confidence: 99%

Radiation from particles with arbitrary energy falling into higher-dimensional black holes

2011

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“…Note that we also used these formulae to produce this kind of check in a generic black-hole binary simulation involving unequal mass and unequal (precessing) spins, the SP6 run in Ref. [10], and obtained satisfactorily agreement. This paper thus provides practical formulae for direct application to extract radiation information from current numerical relativity simulations of compact sources.…”

Section: Discussionmentioning

confidence: 99%

“…The total radiated angular momentum for each configuration is reported in Table I. We ran the S0X and S0Y configurations with our new AMR code [10] with 9 levels of refinement and central resolution of M/40. We extracted the waveform at radii r = 25M , 30M , 35M , and 40M .…”

Section: Numerical Testsmentioning

confidence: 99%

“…The feasibility of evolving generic black-hole binaries was demonstrated in [10] where unexpectedly large recoil velocities of the merger remnant [10,11] were found. One of the important methods to measure the accuracy of the full numerical evolutions is to monitor the conservation of the energy, linear momentum, and angular momentum.…”

Section: Introductionmentioning

confidence: 99%

“…We extend the computation of the radiated angular momentum to all the three Cartesian components. These are useful to verify the conservation of the angular momentum in generic black-hole binaries, for instance, when spin precession is present [10,11,16].…”

Section: Introductionmentioning

confidence: 99%

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Practical formula for the radiated angular momentum

Lousto

Zlochower

2007

Phys. Rev. D

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We present a simple formula for the radiated angular momentum based on a spin-weighted spherical harmonic decomposition of the Weyl scalar ψ4 representing outgoing radiation in the Kinnersley tetrad. We test our formula by measuring the radiated angular momentum from three simulations of non-spinning equal-mass black-hole binaries with orbital angular momentum aligned along the x, y, and z axes respectively. We find that the radiated angular momentum agrees with the differences in the remnant horizon spins and the initial angular momentum for each system.

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Next‐to‐next‐to‐leading order post‐Newtonian linear‐in‐spin binary Hamiltonians

2013

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The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter-only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short-range behavior of the integrands around the sources. The Hamiltonian of a test-spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post-Newtonian approximate) Poincaré algebra are applied. Along the way a self-contained overview for the computation of the 3PN ADM point-mass Hamiltonian is provided, too. 3641 947 102 1 The following literature and in particular [88] gives a complete overview over the research area of parameterization. See e.g. [89] for a point-mass 1PN parameterization, [90] for a point-mass 2PN parameterization, [91] for a quasi-Keplerian 3PN point-mass parameterization, [92, 93] for point-mass parameterizations under leading order spin-orbit coupling, [94] for using a 3PN point-mass parameterization including radiative dynamics for the phasing of gravitational waves, [95] for a post-equal-mass parameterization of a binary at 3PN point-mass level under leading order spin-orbit coupling, and finally [96] for a parameterization up to 2.5PN with orbital angular momentum aligned spins. [97] incorporates the linear-in-spin Hamiltonians given in the present article into the orbital elements for orbital momentum aligned spins.3 series. Such a resummation was successfully implemented into the effective-one-body approach, which analytically provides complete gravitational waveforms for binary inspiral that are in good agreement with numerical relativity. This succeeded so far for point-masses [127,128] and for non-precessing spins [129] by calibrations to full numerical simulations, but more work is needed for precessing spins [130,131]. Here the Hamiltonians derived in the present paper should be very useful, and the spin-orbit one was indeed already incorporated into the effective-one-body approach [132,133]. See also [134] for a very complete overview of the literature on the effective-one-body approach. Alternative ways of resumming the post-Newtonian series by Padé approximants are possible, which is most interesting for certain gauge invariant quantities [135,136]. Within the overlap region of post-Newtonian approximation and numerical relativity in which the gravitational field is not too strong and the number of orbits can be handled by numerical simulations the results of both approaches can be compared. The mentioned resummation methods can make these approximate results competitive ...

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Close encounters of three black holes

Cited by 49 publications

References 54 publications

Radiation from particles with arbitrary energy falling into higher-dimensional black holes

Radiation from particles with arbitrary energy falling into higher-dimensional black holes

Practical formula for the radiated angular momentum

Next‐to‐next‐to‐leading order post‐Newtonian linear‐in‐spin binary Hamiltonians

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