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- W2531435488 abstract "We prove that the essential smoothness of the gravitational metric at shock waves in GR, a PDE regularity issue for weak solutions of the Einstein equations, is determined by a geometrical condition which we introduce and name the {it Riemann-flat condition}. The Riemann-flat condition determines whether or not the essential smoothness of the gravitational metric is two full derivatives more regular than the Riemann curvature tensor. This provides a geometric framework for the open problem as to whether {it regularity singularities} (points where the curvature is in $L^infty$ but the essential smoothness of the gravitational metric is only Lipschitz continuous) can be created by shock wave interaction in GR, or whether metrics Lipschitz at shocks can always be smoothed one level to $C^{1,1}$ by coordinate transformation. As a corollary of the ideas we give a proof that locally inertial frames always exist in a natural sense for shock wave metrics in spherically symmetric spacetimes, independent of whether the metric itself can be smoothed to $C^{1,1}$ locally. This latter result yields an explicit procedure (analogous to Riemann Normal Coordinates in smooth spacetimes) for constructing locally inertial coordinates for Lipschitz metrics, and is a new regularity result for GR solutions constructed by the Glimm scheme." @default.
- W2531435488 created "2016-10-21" @default.
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- W2531435488 date "2016-10-07" @default.
- W2531435488 modified "2023-09-26" @default.
- W2531435488 title "Whether the Metric is Essentially Smooth at Shock Waves in General Relativity Depends on a Hidden Geometric Structure" @default.
- W2531435488 hasPublicationYear "2016" @default.
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