Singularity theorems and the inclusion of torsion in affine theories of gravity

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 presenc...

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Bibliographic Details
Published in:Journal of mathematical physics 2020-01, Vol.61 (1)
Main Authors: Luz, Paulo, Mena, Filipe C.
Format: Article
Language:English
Subjects:
Congruences
Energy conservation
Gravitation
Hyperspaces
Manifolds (mathematics)
Physics
Relativity
Scalars
Singularities
Theorems
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5126220