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- W2595888081 abstract "We prove a necessary and sufficient condition for determining the essential smoothness of weak solutions of the Einstein equations at apparent singularities where the gravitational metric tensor is only Lipschitz continuous, but the tensor is in $L^{infty}$, a regularity so low that locally inertial frames might not exist. Namely, we prove that the question whether there exists a coordinate transformation which smooths a metric from $C^{0,1}$ to $C^{1,1}$ in a neighborhood of a point is equivalent to the condition that the singular part of the metric connection can be extended to a Riemann flat connection in that neighborhood. This applies to shock-wave solutions in General Relativity, and the framework leads to a definition of the curvature of the singular part of a connection, (i.e., the of the shock-set), and we prove that this vanishes if and only if the spacetime metric can be smoothed within the $C^{1,1}$ atlas. As an application of our method we prove that locally inertial frames always exist in a natural sense for shock wave metrics in spherically symmetric spacetimes, a new regularity result for the Glimm scheme, independent of whether the metric itself can be smoothed in a neighborhood." @default.
- W2595888081 created "2017-03-23" @default.
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- W2595888081 date "2016-10-07" @default.
- W2595888081 modified "2023-09-27" @default.
- W2595888081 title "Shock Wave Interactions in General Relativity: The Geometry behind Metric Smoothing and the Existence of Locally Inertial Frames" @default.
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