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Singularity theorems and the inclusion of torsion in affine theories of gravity
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We extend the scope of the Raychaudhuri-Komar singularity theorem of General Relativity to affine theories of gravity with and without torsion. We first generalize the existing focusing theorems using time-like and null congruences of curves which are hypersurface orthogonal, showing how the presence of torsion affects the formation of focal points in Lorentzian manifolds. Considering the energy conservation on a given affine gravity theory, we prove new singularity theorems for accelerated curves in the cases of Lorentzian manifolds containing perfect fluids or scalar field matter sources.
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Cited by 2 Pith papers
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Locally Rotationally Symmetric Spacetimes in Einstein-Cartan Theory and Their Classification
A complete covariant system plus a four-class taxonomy for locally rotationally symmetric spacetimes with Weyssenhoff-fluid torsion, with new Gödel-type, silent, and canonical-vacuum solutions.
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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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