On the topology of stable causality

1989 ◽  
Vol 21 (1) ◽  
pp. 45-59 ◽  
Author(s):  
E. Aguirre-Dabán ◽  
M. Gutiérrez-López
Keyword(s):  
Stable Causality

scholarly journals Stable causality of Black Saturns

2011 ◽  
Vol 2011 (5) ◽  
Author(s):  
Sebastian J. Szybka
Keyword(s):  
Stable Causality

Projection diagrams

2020 ◽  
pp. 280-311
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Spherically Symmetric ◽  
Two Dimensional ◽  
Global Hyperbolicity ◽  
Spacetime Metric ◽  
Stable Causality ◽  
Causal Nature

In this chapter we show that one can usefully represent classes of non-spherically symmetric geometries in terms of two-dimensional diagrams, called projection diagrams, using an auxiliary two-dimensional metric constructed out of the spacetime metric. Whenever such a construction can be carried out, the issues such as stable causality, global hyperbolicity, the existence of event or Cauchy horizons, the causal nature of boundaries, and the existence of conformally smooth infinities become evident by inspection of the diagrams.

scholarly journals Causal hierarchy in modified gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Raúl Carballo-Rubio ◽  
Francesco Di Filippo ◽  
Stefano Liberati ◽  
Matt Visser
Keyword(s):  
Modified Gravity ◽  
Modified Theories Of Gravity ◽  
Global Hyperbolicity ◽  
Signal Velocity ◽  
Superluminal Propagation ◽  
Strong Causality ◽  
Theories Of Gravity ◽  
Stable Causality ◽  
Multiple Metrics ◽  
Extra Structure

Abstract We investigate the causal hierarchy in various modified theories of gravity. In general relativity the standard causal hierarchy, (key elements of which are chronology, causality, strong causality, stable causality, and global hyperbolicity), is well-established. In modified theories of gravity there is typically considerable extra structure, (such as: multiple metrics, aether fields, modified dispersion relations, Hořava-like gravity, parabolic propagation, etcetera), requiring a reassessment and rephrasing of the usual causal hierarchy. We shall show that in this extended framework suitable causal hierarchies can indeed be established, and discuss the implications for the interplay between “superluminal” propagation and causality. The key distinguishing feature is whether the signal velocity is finite or infinite. Preserving even minimal notions of causality in the presence of infinite signal velocity requires the aether field to be both unique and hypersurface orthogonal, leading us to introduce the notion of global parabolicity.

scholarly journals Causality theory for closed cone structures with applications

2019 ◽  
Vol 31 (05) ◽  
pp. 1930001 ◽  
Author(s):  
Ettore Minguzzi
Keyword(s):  
Minkowski Spacetime ◽  
Regularity Conditions ◽  
Lorentzian Manifolds ◽  
Global Hyperbolicity ◽  
Singularity Theorems ◽  
Minkowski Spaces ◽  
Closed Cone ◽  
Stable Causality ◽  
Increasing Functions

We develop causality theory for upper semi-continuous distributions of cones over manifolds generalizing results from mathematical relativity in two directions: non-round cones and non-regular differentiability assumptions. We prove the validity of most results of the regular Lorentzian causality theory including: causal ladder, Fermat’s principle, notable singularity theorems in their causal formulation, Avez–Seifert theorem, characterizations of stable causality and global hyperbolicity by means of (smooth) time functions. For instance, we give the first proof for these structures of the equivalence between stable causality, [Formula: see text]-causality and existence of a time function. The result implies that closed cone structures that admit continuous increasing functions also admit smooth ones. We also study proper cone structures, the fiber bundle analog of proper cones. For them, we obtain most results on domains of dependence. Moreover, we prove that horismos and Cauchy horizons are generated by lightlike geodesics, the latter being defined through the achronality property. Causal geodesics and steep temporal functions are obtained with a powerful product trick. The paper also contains a study of Lorentz–Minkowski spaces under very weak regularity conditions. Finally, we introduce the concepts of stable distance and stable spacetime solving two well-known problems (a) the characterization of Lorentzian manifolds embeddable in Minkowski spacetime, they turn out to be the stable spacetimes, (b) the proof that topology, order and distance (with a formula à la Connes) can be represented by the smooth steep temporal functions. The paper is self-contained, in fact we do not use any advanced result from mathematical relativity.

scholarly journals Stable causality of the Pomeransky–Senkov black holes

2011 ◽  
Vol 15 (1) ◽  
pp. 175-178 ◽  
Author(s):  
Piotr T. Chrúsciel ◽  
Sebastian J. Szybka
Keyword(s):  
Black Holes ◽  
Stable Causality

The existence of cosmic time functions

1969 ◽  
Vol 308 (1494) ◽  
pp. 433-435 ◽  
Keyword(s):  
Cosmic Time ◽  
Space Time ◽  
Time Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Null Curve ◽  
Null Curves ◽  
Stable Causality ◽  
Necessary And Sufficient

It is shown that stable causality is the necessary and sufficient condition that there should exist a cosmic time function which increases along every future directed timelike or null curve. Stable causality means that there are no closed timelike or null curves in any Lorentz metric that is sufficiently close to the space-time metric.

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