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Dynamical extensions for shell-crossing singularities
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We derive global weak solutions of Einstein's equations for spherically symmetric dust-filled space-times which admit shell-crossing singularities. In the marginally bound case, the solutions are weak solutions of a conservation law. In the non-marginally bound case, the equations are solved in a generalized sense involving metric functions of bounded variation. The solutions are not unique to the future of the shell-crossing singularity, which is replaced by a shock wave in the present treatment; the metric is bounded but not continuous.
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Cited by 2 Pith papers
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Quantum gravitational stellar evolution beyond shell-crossing singularities
A Hamiltonian formulation of Darmois-Israel junction conditions extends LQG-inspired stellar collapse models beyond shell-crossing singularities by treating them as timelike thin dust shells, yielding an inter-univers...
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Non-uniqueness of the shockwave dynamics in effective loop quantum gravity
In effective loop quantum gravity, an infinite family of mathematically equivalent collapse equations produce different weak solutions after shell crossing, so the predicted black hole lifetime (e.g., M^2, M^3, M^4) i...
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