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Pré-Publication, Document De Travail Année : 2023

On homogeneous plane waves

Résumé

Plane waves are a special class of Lorentzian spaces and of a great importance in physics and in general relativity. Here we consider $1$-connected non-flat homogeneous plane waves, and we essentially establish a correspondence between these spaces and certain $1$-parameter groups of automorphisms of Heisenberg. It is well known that plane waves admit an infinitesimal Heisenberg action. We show here that this action integrates to a global one under the homogeneity assumption, and as a consequence, we obtain the form of the identity component of the isometry group of a $1$-connected non-flat homogeneous plane wave. Using the Heisenberg global action, we show that a $1$-connected homogeneous plane wave has global Brinkmann coordinates.

Dates et versions

hal-04411467 , version 1 (23-01-2024)

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Malek Hanounah, Lilia Mehidi, Abdelghani Zeghib. On homogeneous plane waves. 2024. ⟨hal-04411467⟩
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