Abstract:For a plane gravitational wave whose profile is given, in Brinkmann coordinates, by a 2 × 2 symmetric traceless matrix K(U ), the matrix Sturm-Liouville equationP = KP plays a multiple and central rôle: (i) it determines the isometries; (ii) it appears as the key tool for switching from Brinkmann to BJR coordinates and vice versa; (iii) it determines the trajectories of particles initially at rest. All trajectories can be obtained from trivial "Carrollian" ones by a suitable action of the (broken) Carrollian i… Show more
“…However, it is not clear how an equivalence can be obtained given that a supertranslation is labelled by a single function on the sphere. the gravitational wave to the probes [45] (see also [46][47][48][49] and references therein). In contrast, the velocity kick/refraction memory that we describe here is specific to the observers close to null infinity and can be described in terms of superboost field transitions.…”
Section: Introduction and Outline Of The Resultsmentioning
We derive a closed-form expression of the orbit of Minkowski spacetime under arbitrary DiffpS 2 q super-Lorentz transformations and supertranslations. Such vacua are labelled by the superboost, superrotation and supertranslation fields. Impulsive transitions among vacua are related to the refraction memory effect and the displacement memory effect. A phase space is defined whose asymptotic symmetry group consists of arbitrary DiffpS 2 q super-Lorentz transformations and supertranslations. It requires a renormalization of the symplectic structure. We show that our final surface charge expressions are consistent with the leading and subleading soft graviton theorems. We contrast the leading BMS triangle structure to the mixed overleading/subleading BMS square structure. 1
“…However, it is not clear how an equivalence can be obtained given that a supertranslation is labelled by a single function on the sphere. the gravitational wave to the probes [45] (see also [46][47][48][49] and references therein). In contrast, the velocity kick/refraction memory that we describe here is specific to the observers close to null infinity and can be described in terms of superboost field transitions.…”
Section: Introduction and Outline Of The Resultsmentioning
We derive a closed-form expression of the orbit of Minkowski spacetime under arbitrary DiffpS 2 q super-Lorentz transformations and supertranslations. Such vacua are labelled by the superboost, superrotation and supertranslation fields. Impulsive transitions among vacua are related to the refraction memory effect and the displacement memory effect. A phase space is defined whose asymptotic symmetry group consists of arbitrary DiffpS 2 q super-Lorentz transformations and supertranslations. It requires a renormalization of the symplectic structure. We show that our final surface charge expressions are consistent with the leading and subleading soft graviton theorems. We contrast the leading BMS triangle structure to the mixed overleading/subleading BMS square structure. 1
The Eisenhart lift of a Paul Trap used to store ions in molecular physics is a linearly polarized periodic gravitational wave. A modified version of Dehmelt's Penning Trap is in turn related to circularly polarized periodic gravitational waves, sought for in inflationary models. Similar equations rule also the Lagrange points in Celestial Mechanics. The explanation is provided by anisotropic oscillators.Phys. Rev. D 98 (2018) no.4, 044037
The isometries of an exact plane gravitational wave are symmetries for both massive and massless particles. Their conformal extensions which are in fact Chrono-Projective transformations introduced by Duval et al are symmetries for massless particles and play an important role for the Memory Effect. The generically 5-parameter isometry group extends under special circumstances to a 6 parameter group, further extended by homotheties, which are universal Chrono-Projective symmetries for any profile.
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