Gravitational Waves: Just Plane Symmetry

Abstract

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also discuss a mini-superspace description of spacetimes with plane wave symmetry.

10 pages, TeX, uses IOP style files

References in corpus (4)

• The Principle of Symmetric Criticality in General Relativity
• Group Invariant Solutions without Transversality and the Principle of Symmetric Criticality
• Group Invariant Solutions Without Transversality
• Michel theory of symmetry breaking and gauge theories

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• Scaling and conformal symmetries for plane gravitational waves
• New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory
• A generalized Noether theorem for scaling symmetry
• Ion Traps and the Memory Effect for Periodic Gravitational Waves
• Particle motion in circularly polarized vacuum pp waves
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• Memory Effect and Carroll Symmetry: 50 years later
• Conformally related vacuum gravitational waves, and their symmetries
• Characterization of three-dimensional Lorentzian metrics that admit four Killing vectors