Introduces a synthetic null energy condition using optimal transport on topological causal spaces that agrees with the classical NEC in smooth cases and enables proofs of area and singularity theorems in non-smooth settings.
arXiv:2209.12736
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Introduces Lorentzian spaces as a weakening of Lorentzian length spaces and considers pointed Gromov-Hausdorff metrics, non-spacetime maximal examples, and canonical Cauchy development representatives.
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On the geometry of synthetic null hypersurfaces
Introduces a synthetic null energy condition using optimal transport on topological causal spaces that agrees with the classical NEC in smooth cases and enables proofs of area and singularity theorems in non-smooth settings.
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Maximality and Cauchy developments of Lorentzian length spaces
Introduces Lorentzian spaces as a weakening of Lorentzian length spaces and considers pointed Gromov-Hausdorff metrics, non-spacetime maximal examples, and canonical Cauchy development representatives.