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Cosmologies with turning points
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We explore singularity-free and geodesically-complete cosmologies based on manifolds that are not quite Lorentzian. The metric can be either smooth everywhere or non-degenerate everywhere, but not both, depending on the coordinate system. The smooth metric gives an Einstein tensor that is first order in derivatives while the non-degenerate metric has a piecewise FLRW form. On such a manifold the universe can transition from expanding to contracting, or vice versa, with the Einstein equations satisfied everywhere and without violation of standard energy conditions. We also obtain a corresponding extension of the Kasner vacuum solutions on such manifolds.
Forward citations
Cited by 2 Pith papers
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Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
Tensionless p-branes and branes in degenerate-metric spacetimes admit symmetry transformations built from Killing tensors of arbitrary rank, extending string W-symmetries to all brane dimensions.
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Complex degenerate metrics in general relativity: a covariant extension of the Moore-Penrose algorithm
A covariant Moore-Penrose algorithm for complex degenerate metrics is formulated, but its uniqueness and torsion interpretation depend on an arbitrary auxiliary metric and the central proof is incomplete.
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