Intrinsic angular momentum for radiating spacetimes which agrees with the Komar integral in the axisymmetric case

Gallo, Emanuel; Moreschi, Osvaldo M.

doi:10.1103/physrevd.89.084009

Cited by 15 publications

(13 citation statements)

References 30 publications

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“…An easy computation (see [GM14] for the analogous computation in the Newman-Penrose formalism and Bondi framework) shows that, in view of our estimates in the I + gauge and the relation between u f and v ∞ , we have the relation:…”

Section: Estimating βmentioning

confidence: 83%

The non-linear stability of the Schwarzschild family of black holes

Dafermos¹,

Holzegel²,

Rodnianski³

et al. 2021

Preprint

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We prove the non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region: general vacuum initial data-with no symmetry assumedsufficiently close to Schwarzschild data evolve to a vacuum spacetime which (i) possesses a complete future null infinity I + (whose past J − (I + ) is moreover bounded by a regular future complete event horizon H + ),(ii) remains close to Schwarzschild in its exterior, and(iii) asymptotes back to a member of the Schwarzschild family as an appropriate notion of time goes to infinity, provided that the data are themselves constrained to lie on a teleologically constructed codimension-3 "submanifold" of moduli space. This is the full nonlinear asymptotic stability of Schwarzschild since solutions not arising from data lying on this submanifold should by dimensional considerations approach a Kerr spacetime with rotation parameter a = 0, i.e. such solutions cannot satisfy (iii). The statement is effective, providing quantitative bounds from explicit initial data quantities, and the global nearness to Schwarzschild at top order can be measured with respect to the same quantity as initial data, i.e. without loss of derivatives. The proof employs teleologically normalised double null gauges, is expressed entirely in physical space and makes essential use of the analysis in our previous study of the linear stability of the Kerr family around Schwarzschild [DHR], as well as techniques developed over the years to control the non-linearities of the Einstein equations, in particular in the difficult radiation zone associated to subtle non-linear effects like Christodoulou memory. The present work, however, is entirely self-contained. In view of the recent [DHR19, TdCSR20], our approach can be applied to the full non-linear asymptotic stability of the subextremal Kerr family.cone which is a level surface of the exterior optical function. This is still compatible with decay of all quantities for fixed r since the "interior" region was covered by a different optical functions whose null cones were not related to the null cones of the exterior optical function. In the exterior region of [CK93], on the other hand, the r decay is sufficient to compensate for the lack of decay for some fully rescaled quantities in u, so as for all nonlinearities to still be controllable.We begin with the point p ∈ S and v ∈ T p S. By a well known result of Klingenberg [Kli59], if in (4.4.1) is sufficiently small, there exists a geodesic polar neighbourhood S p, 7 8 π ⊂ S around p of, say, radius 7 8 π. Let us denote the chart by the diffeomorphism ϕ p, 7 8 π : S p, 7 8 π → D 7 8 π .Associated to this chart are geodesic polar coordinates which we shall denote as (θ, φ). These are uniquely determined by declaring that φ = 0 corresponds to the direction ∂ v and the frame ∂ θ , ∂ φ is compatible with the orientation where defined. Let γ(s) denote the geodesic in S with initial condition γ(0) = p, γ (0) = v. This is parametrised by arc length. ...

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Section: Estimating βmentioning

confidence: 83%

The non-linear stability of the Schwarzschild family of black holes

Dafermos¹,

Holzegel²,

Rodnianski³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…It is also appealing to define an intrinsic angular momentum which is independent from supertranslations. Such an intrinsic angular momentum was defined in [86] using an implicit dressing procedure; see also [87,88] for another construction. We will provide the explicit definition of the supertranslation-invariant intrinsic angular momentum in terms of Bondi fields in section 5 for non-radiative configurations.…”

Section: Jhep10(2020)116mentioning

confidence: 99%

“…Instead, we proposed a two-parameter prescription for covariantly defining the center-of-mass, which leads to a new expression for the flux of the center-of-mass to all orders in the radiative multipole expansion. Furthermore, we proposed the supertranslation-invariant definition of Lorentz charges -the intrinsic Lorentz charges -for non-radiative configurations, which provides an explicit realization of the dressing procedure described in [86] (see also [87,88]).…”

Section: Jhep10(2020)116mentioning

confidence: 99%

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

Compère

Oliveri

Seraj

2020

J. High Energ. Phys.

127

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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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“…While all of these agree on their l < 2 modes, 15 the Moreschi supermomentum is the supermomentum that can most easily be used to map to the super rest frame for reasons discussed in [15][16][17]48].…”

Section: Appendix: Fixing the Supertranslation Freedom With The Moreschi Supermomentummentioning

confidence: 99%

Fixing the BMS frame of numerical relativity waveforms

et al. 2021

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Understanding the Bondi-Metzner-Sachs (BMS) frame of the gravitational waves produced by numerical relativity is crucial for ensuring that analyses on such waveforms are performed properly. It is also important that models are built from waveforms in the same BMS frame. Up until now, however, the BMS frame of numerical waveforms has not been thoroughly examined, largely because the necessary tools have not existed. In this paper, we show how to analyze and map to a suitable BMS frame for numerical waveforms calculated with the Spectral Einstein Code (SpEC). However, the methods and tools that we present are general and can be applied to any numerical waveforms. We present an extensive study of 13 binary black hole systems that broadly span parameter space. From these simulations, we extract the strain and also the Weyl scalars using both SpECTRE's Cauchy-characteristic extraction module and also the standard extrapolation procedure with a displacement memory correction applied during postprocessing. First, we show that the current center-of-mass correction used to map these waveforms to the center-ofmass frame is not as effective as previously thought. Consequently, we also develop an improved correction that utilizes asymptotic Poincaré charges instead of a Newtonian center-of-mass trajectory. Next, we map our waveforms to the post-Newtonian (PN) BMS frame using a PN strain waveform. This helps us find the unique BMS transformation that minimizes the L 2 norm of the difference between the numerical and PN strain waveforms during the early inspiral phase. We find that once the waveforms are mapped to the PN BMS frame, they can be hybridized with a PN strain waveform much more effectively than if one used any of the previous alignment schemes, which only utilize the Poincaré transformations.

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Intrinsic angular momentum for radiating spacetimes which agrees with the Komar integral in the axisymmetric case

Cited by 15 publications

References 30 publications

The non-linear stability of the Schwarzschild family of black holes

The non-linear stability of the Schwarzschild family of black holes

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

Fixing the BMS frame of numerical relativity waveforms

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