Supertranslations and holographic stress tensor

Virmani, Amitabh

doi:10.1007/jhep02(2012)024

Cited by 7 publications

(6 citation statements)

References 72 publications

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“…In this section we introduce our notion of asymptotic flatness at timelike infinity. It is based on the corresponding notion introduced by Beig and Schmidt [41,42] at spatial infinity, which has been extensively studied over the years [43][44][45][46][47]. We work with a coordinate based definition.…”

Section: Asymptotic Flatness At Timelike Infinitymentioning

confidence: 99%

“…(2.22), are missing there. We note that the action of supertranslations at the second order has not been much discussed in the literature; comments appear in [46,47], though neither of these papers present any details on this specific calculation. We hope that the reader will find our appendices B and D useful.…”

Section: Asymptotic Expansion Of the Equation Of Motionmentioning

confidence: 99%

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Supertranslations at timelike infinity

Chakraborty

Ghosh

Hoque

et al. 2022

J. High Energ. Phys.

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We propose a definition of asymptotic flatness at timelike infinity in four spacetime dimensions. We present a detailed study of the asymptotic equations of motion and the action of supertranslations on asymptotic fields. We show that the Lee-Wald symplectic form Ω(g, δ1g, δ2g) does not get contributions from future timelike infinity with our boundary conditions. As a result, the “future charges” can be computed on any two-dimensional surface surrounding the sources at timelike infinity. We present expressions for supertranslation and Lorentz charges.

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Section: Asymptotic Flatness At Timelike Infinitymentioning

confidence: 99%

Section: Asymptotic Expansion Of the Equation Of Motionmentioning

confidence: 99%

Supertranslations at timelike infinity

Chakraborty

Ghosh

Hoque

et al. 2022

J. High Energ. Phys.

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“…For asymptotically flat spacetimes, the asymptotic symmetry group at spatial infinity is the BMS group, consisting of supertranslations and Lorentz transformations, which contains the Poincaré group as a subgroup [13,14,48,[50][51][52][53][54][55][56][57][58][59]:…”

Section: Asymptotic Symmetry Group =mentioning

confidence: 99%

Gravitational multipole moments from Noether charges

Compère

Oliveri

Seraj

2018

J. High Energ. Phys.

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Abstract:We define the mass and current multipole moments for an arbitrary theory of gravity in terms of canonical Noether charges associated with specific residual transformations in canonical harmonic gauge, which we call multipole symmetries. We show that our definition exactly matches Thorne's mass and current multipole moments in Einstein gravity, which are defined in terms of metric components. For radiative configurations, the total multipole charges -including the contributions from the source and the radiation -are given by surface charges at spatial infinity, while the source multipole moments are naturally identified by surface integrals in the near-zone or, alternatively, from a regularization of the Noether charges at null infinity. The conservation of total multipole charges is used to derive the variation of source multipole moments in the near-zone in terms of the flux of multipole charges at null infinity.

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“…Conversely, a parityirregular transformation [i.e., when K a (n b ) has even or indefinite parity] is one in which ξ α contains supertranslations that do alter the position of the particle, and a parity-irregular MP is one related to a parity-regular MP by a parity-irregular transformation. Historically, parityirregular supertranslations have created challenges [36][37][38][39] in canonical descriptions of spacetimes, as well as in defining angular momentum, because the group of supertranslations is infinite, while we would wish for a canonical 3-momentum, for example, to be associated with the three-dimensional group of translations. Here we might have similar problems in a canonical description of the motion of the small object.…”

Section: Gauge and Motionmentioning

confidence: 99%

Gravitational self-force from radiation-gauge metric perturbations

2014

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Calculations of the gravitational self-force (GSF) on a point mass in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the metric perturbation is formulated in a class of "radiation" gauges, in which the particle singularity is non-isotropic and extends away from the particle's location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We show that three types of radiation gauge exist: two containing a radial string-like singularity emanating from the particle, either in one direction ("half-string" gauges) or both directions ("full-string" gauges); and a third type containing no strings but with a jump discontinuity (and possibly a delta function) across a surface intersecting the particle. Based on a flat-space example, we argue that the standard mode-by-mode reconstruction procedure yields the "regular half" of a half-string solution, or (equivalently) either of the regular halves of a no-string solution. For the half-string case, we formulate the GSF in a locally deformed radiation gauge that removes the string singularity near the particle. We derive a mode-sum formula for the GSF in this gauge, which is analogous to the standard Lorenz-gauge formula but requires a correction to the values of the regularization parameters. For the no-string case, we formulate the GSF directly, without a local deformation, and we derive a mode-sum formula that requires no correction to the regularization parameters but involves a certain averaging procedure. We explain the consistency of our results with Gralla's invariance theorem for the regularization parameters, and we discuss the correspondence between our method and a related approach by Friedman et al.

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Supertranslations and holographic stress tensor

Cited by 7 publications

References 72 publications

Supertranslations at timelike infinity

Supertranslations at timelike infinity

Gravitational multipole moments from Noether charges

Gravitational self-force from radiation-gauge metric perturbations

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