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arXiv · 2001.01806

Distributional Metrics and the Action Principle of Einstein-Hilbert Gravity

Albert Huber
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Abstract

In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry. Considering Colombeau's nonlinear theory of generalized functions, this result is extended to apply to an associated class of distributional Kerr-Schild geometries, and then used to formulate a variational principle for these singular spacetimes. More specifically, it is shown in this regard that a variation of a suitably regularized Einstein-Hilbert action can be performed even if the metric of one of the corresponding generalized Kerr-Schild representatives contains a generalized delta function that converges in a suitable limit to a delta distribution.

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Albert Huber. 2020-01-06. Distributional Metrics and the Action Principle of Einstein-Hilbert Gravity. https://doi.org/10.1088/1361-6382%2Fab7614

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