On differentiability of volume time functions

DOI10.1007/s00023-015-0448-3zbMath1351.83006arXiv1301.2909OpenAlexW1918118557MaRDI QIDQ331475

Ettore Minguzzi, James D. E. Grant, Piotr T. Chrusciel

Publication date: 27 October 2016

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.2909

zbMATH Keywords

differentiabilityglobally hyperbolic manifoldscausal curvesGeroch's volume functionHawking's time functionLipschitz time functionslocal anti-Lipschitz conditionvolume time functions

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Equations of motion in general relativity and gravitational theory (83C10)

Related Items

The null distance encodes causality ⋮ Causality for nonlocal phenomena ⋮ Lorentzian manifolds properly isometrically embeddable in Minkowski spacetime ⋮ Global hyperbolicity through the eyes of the null distance ⋮ On the regularity of Cauchy hypersurfaces and temporal functions in closed cone structures ⋮ Lyapounov functions of closed cone fields: from Conley theory to time functions ⋮ Globally hyperbolic spacetimes can be defined without the ‘causal’ condition ⋮ Structure of globally hyperbolic spacetimes-with-timelike-boundary ⋮ Lorentzian causality theory ⋮ Causality theory for closed cone structures with applications ⋮ Lorentzian Gromov-Hausdorff theory and finiteness results ⋮ Globally hyperbolic spacetimes: slicings, boundaries and counterexamples

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Time functions as utilities
• Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions
• Characterization of some causality conditions through the continuity of the Lorentzian distance
• \(K\)-causality coincides with stable causality
• Smoothing and extending cosmic time functions
• Conformal changes and geodesic completeness
• On the structure of singular sets of convex functions
• On smooth Cauchy hypersurfaces and Geroch's splitting theorem
• Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
• Global hyperbolicity is stable in the interval topology
• On smooth time functions
• The Lipschitz continuity of the distance function to the cut locus
• Cauchy horizon end points and differentiability
• A causal order for spacetimes with Lorentzian metrics: proof of compactness of the space of causal curves
• Limit curve theorems in Lorentzian geometry
• The existence of cosmic time functions
• Domain of Dependence
• The Large Scale Structure of Space-Time
• Ordinary Differential Equations
• Regularity of horizons and the area theorem