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On the geometry of impulsive gravitational waves
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We describe impulsive gravitational pp-waves entirely in the distributional picture. Applying Colombeau's nonlinear framework of generalized functions we handle the formally ill-defined products of distributions which enter the geodesic as well as the geodesic deviation equation. Using a universal regularization procedure we explicitly derive regularization independent distributional limits. In the special case of impulsive plane waves we compare our results with the particle motion derived from the continuous form of the metric.
Forward citations
Cited by 2 Pith papers
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Generalizing the Penrose cut-and-paste method: Null shells with pressure and energy flux
The Penrose cut-and-paste method is generalized to null thin shells with arbitrary matter content, including pressure and energy flux, via a locally Lipschitz metric and a Dirac-delta coordinate transformation.
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Memory Effect for deformed gravitational waves
Displacement memory in squeezed Pöschl–Teller gravitational waves is lost in the finite-amplitude impulsive limit; restoring it requires amplitudes that diverge as the squeezing parameter p→∞.
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