Distance to a focal point and singularity theorems with weak timelike convergence condition

DOI10.1017/S0305004108001825zbMath1161.53019MaRDI QIDQ3616244

Seong-Hun Paeng

Publication date: 24 March 2009

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

Ricci curvaturevolume formtime-like convergence

Mathematics Subject Classification ID

Applications of local differential geometry to the sciences (53B50) Astronomy and astrophysics (85A99) Equations of motion in general relativity and gravitational theory (83C10) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (4)

The upperbound of the volume expansion rate in a Lorentzian manifold ⋮ Volume comparison between spacelike hypersurfaces in a Lorentzian manifold with integral Ricci curvature bounds ⋮ Gaussian curvature, elasticity of string and geodesic incompleteness in string theory ⋮ Hawking's singularity theorem under a bounded integral norm of Ricci curvature

Cites Work

• Volume expansion rate of the Lorentzian manifold based on integral Ricci curvature over a timelike geodesic
• Some results on the occurrence of compact minimal submanifolds
• General relativity and conjugate ordinary differential equations
• Relative volume comparison with integral curvature bounds
• The singularities of gravitational collapse and cosmology

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