Compact binary coalescences: The subtle issue of angular momentum

Ashtekar, Abhay; Lorenzo, Tommaso De; Khera, Neev

doi:10.1103/physrevd.101.044005

“…Consequently, since the magnetic memory does not have such terms, one might presume that the magnetic memory vanishes, i.e., that the net change in the magnetic component of the strain is zero. Currently, this is unknown [18,[33][34][35]. But, it is known that the retarded time integral of the magnetic memory does not vanish; this is what we refer to as the spin memory effect.…”

Section: Magnetic Memorymentioning

confidence: 98%

Computation of displacement and spin gravitational memory in numerical relativity

Mitman

¹

,

Moxon

²

,

Scheel

³

et al. 2020

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We present the first numerical relativity waveforms for binary black hole mergers produced using spectral methods that show both the displacement and the spin memory effects. Explicitly, we use the SXS (Simulating eXtreme Spacetimes) Collaboration's SpEC code to run a Cauchy evolution of a binary black hole merger and then extract the gravitational wave strain using SpECTRE's version of a Cauchycharacteristic extraction. We find that we can accurately resolve the strain's traditional m ¼ 0 memory modes and some of the m ≠ 0 oscillatory memory modes that have previously only been theorized. We also perform a separate calculation of the memory using equations for the Bondi-Metzner-Sachs charges as well as the energy and angular momentum fluxes at asymptotic infinity. Our new calculation uses only the gravitational wave strain and two of the Weyl scalars at infinity. Also, this computation shows that the memory modes can be understood as a combination of a memory signal throughout the binary's inspiral and merger phases, and a quasinormal mode signal near the ringdown phase. Additionally, we find that the magnetic memory, up to numerical error, is indeed zero as previously conjectured. Last, we find that signalto-noise ratios of memory for LIGO, the Einstein Telescope, and the Laser Interferometer Space Antenna with these new waveforms and new memory calculation are larger than previous expectations based on post-Newtonian or minimal waveform models.

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“…In the last stage of this work, we noticed [32] where a related expression is derived in another formalism, which remains to be compared with eq. (5.11).…”

Section: The Final Boosted and Supertranslated Kerr Metricmentioning

confidence: 99%

“…We derived the explicit expressions for the BMS charges for the initial and final states u → ±∞ of black hole mergers in terms of Bondi quantities. A comparison with the geometric expressions derived in [32] remains to be performed. We derived the BMS fluxbalance laws in terms of radiative multipole moments.…”

Section: Jhep10(2020)116mentioning

confidence: 99%

“…The extended BMS fluxbalance laws are complete at second order in the large radius expansion, in the sense that no other evolution equation arises from Einstein's equations in Bondi gauge at that order, though an infinite tower of subleading flux-balance laws are implied by Einstein's equations [9,23]. While such leading and subleading flux-balance laws have already appeared in the literature [3,9,20,[24][25][26][27][28][29][30][31][32], no unified presentation has yet been given that provides a comprehensive first-principle derivation of all BMS laws for standard asymptotically flat spacetimes which includes their explicit relationship to memory effects. The first objective of this paper is to provide such a unified presentation, complementing the remarkable work of Nichols [27,28].…”

Section: Introduction and Outlinementioning

confidence: 99%

“…The proper supermomentum flux-balance laws instead allow to deduce the total displacement memory as a function of the radiation and initial parameters of the merger [24,[44][45][46][47][48]. The Lorentz flux-balance laws similarly allow to deduce the final angular momentum and center-of-mass shift after the merger, though the choice of the supertranslation and Lorentz frame introduces complications [32]. Finally, the super-Lorentz flux-balance laws allow to deduce the spin and center-of-mass memories [27,28].…”

Section: Introduction and Outlinementioning

confidence: 99%

See 2 more Smart Citations

The Poincaré and BMS flux-balance laws with application to binary systems

Compère

¹

,

Oliveri

²

,

Seraj

³

2020

J. High Energ. Phys.

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Asymptotically flat spacetimes admit both supertranslations and Lorentz transformations as asymptotic symmetries. Furthermore, they admit super-Lorentz transformations, namely superrotations and superboosts, as outer symmetries associated with super-angular momentum and super-center-of-mass charges. In this paper, we present comprehensively the flux-balance laws for all such BMS charges. We distinguish the Poincaré flux-balance laws from the proper BMS flux-balance laws associated with the three relevant memory effects defined from the shear, namely, the displacement, spin and center-of-mass memory effects. We scrutinize the prescriptions used to define the angular momentum and center-of-mass. In addition, we provide the exact form of all Poincaré and proper BMS flux-balance laws in terms of radiative symmetric tracefree multipoles. Fluxes of energy, angular momentum and octupole super-angular momentum arise at 2.5PN, fluxes of quadrupole supermomentum arise at 3PN and fluxes of momentum, center-of-mass and octupole super-center-of-mass arise at 3.5PN. We also show that the BMS flux-balance laws lead to integro-differential consistency constraints on the radiation-reaction forces acting on the sources. Finally, we derive the exact form of all BMS charges for both an initial Kerr binary and a final Kerr black hole in an arbitrary Lorentz and supertranslation frame, which allows to derive exact constraints on gravitational waveforms produced by binary black hole mergers from each BMS flux-balance law.

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Unified treatment of null and spatial infinity IV: angular momentum at null and spatial infinity

Ashtekar,

Khera

2024

J. High Energ. Phys.

4

0

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In a companion paper [1] we introduced the notion of asymptotically Minkowski spacetimes. These space-times are asymptotically flat at both null and spatial infinity, and furthermore there is a harmonious matching of limits of certain fields as one approaches i° in null and space-like directions. These matching conditions are quite weak but suffice to reduce the asymptotic symmetry group to a Poincaré group $$ {\mathfrak{p}}_{i{}^{\circ}} $$ p i ° . Restriction of $$ {\mathfrak{p}}_{i{}^{\circ}} $$ p i ° to future null infinity $$ {\mathcal{I}}^{+} $$ I + yields the canonical Poincaré subgroup $$ {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{bms}} $$ p i ° bms of the BMS group $$ \mathfrak{B} $$ B selected in [2, 3] and that its restriction to spatial infinity i°, the canonical subgroup $$ {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{spi}} $$ p i ° spi of the Spi group $$ \mathfrak{S} $$ S selected in [4, 5]. As a result, one can meaningfully compare angular momentum that has been defined at i° using $$ {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{spi}} $$ p i ° spi with that defined on $$ {\mathcal{I}}^{+} $$ I + using $$ {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{bms}} $$ p i ° bms . We show that the angular momentum charge at i° equals the sum of the angular momentum charge at any 2-sphere cross-section S of $$ {\mathcal{I}}^{+} $$ I + and the total flux of angular momentum radiated across the portion of $$ {\mathcal{I}}^{+} $$ I + to the past of S. In general the balance law holds only when angular momentum refers to SO(3) subgroups of the Poincaré group $$ {\mathfrak{p}}_{i{}^{\circ}} $$ p i ° .

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Compact binary coalescences: The subtle issue of angular momentum

Cited by 40 publications

References 42 publications

Computation of displacement and spin gravitational memory in numerical relativity

Computation of displacement and spin gravitational memory in numerical relativity

The Poincaré and BMS flux-balance laws with application to binary systems

Unified treatment of null and spatial infinity IV: angular momentum at null and spatial infinity

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