Synthetic timelike Ricci bounds TCD^e_p(K,N) are stable under C^0-limits of Lorentzian metrics, with applications to impulsive gravitational waves and counterexamples to Lorentzian splitting theorems.
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Causally simple spacetimes with continuous Lorentzian metrics on smooth manifolds are infinitesimally Minkowskian.
A Hausdorff-type metric is placed on the space of Cauchy hypersurfaces in globally hyperbolic spacetimes, yielding completeness and local compactness results that generalize earlier work by Beem and Takahashi.
In synthetic Lorentzian spaces, the timelike curvature dimension condition TCD_q(K,N) is equivalent to the timelike Brunn-Minkowski inequality TBM_q(K,N) in the q-essentially non-branching case, with a similar equivalence for the entropic version.
An analogue of Reshetnyak's majorisation theorem is proven for Lorentzian length spaces with upper curvature bounds, yielding a four-point characterization of those bounds suitable for discrete settings.
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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Stability of Synthetic Timelike Ricci Bounds under $C^0$-Limits and Applications to Impulsive Gravitational Waves
Synthetic timelike Ricci bounds TCD^e_p(K,N) are stable under C^0-limits of Lorentzian metrics, with applications to impulsive gravitational waves and counterexamples to Lorentzian splitting theorems.
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Infinitesimal Minkowskianity for manifolds with continuous Lorentzian metrics
Causally simple spacetimes with continuous Lorentzian metrics on smooth manifolds are infinitesimally Minkowskian.
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Hausdorff-type metric geometry of the space of Cauchy hypersurfaces
A Hausdorff-type metric is placed on the space of Cauchy hypersurfaces in globally hyperbolic spacetimes, yielding completeness and local compactness results that generalize earlier work by Beem and Takahashi.
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The equivalence between timelike Ricci curvature and the timelike Brunn Minkowski inequality on synthetic Lorentzian spaces
In synthetic Lorentzian spaces, the timelike curvature dimension condition TCD_q(K,N) is equivalent to the timelike Brunn-Minkowski inequality TBM_q(K,N) in the q-essentially non-branching case, with a similar equivalence for the entropic version.
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Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces
An analogue of Reshetnyak's majorisation theorem is proven for Lorentzian length spaces with upper curvature bounds, yielding a four-point characterization of those bounds suitable for discrete settings.
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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.