On global hyperbolicity of spacetimes: some recent advances and open problems. (English) Zbl 1503.53130
Parasidis, Ioannis. N. (ed.) et al., Mathematical analysis in interdisciplinary research. Cham: Springer. Springer Optim. Appl. 179, 281-295 (2021).
Summary: This chapter is an up-to-date account of results on globally hyperbolic spacetimes and serves as a multitool; we start the exposition of results from a foundational level, where the main tools are order-theory and general topology, we continue with results of a more geometric nature, and we finally reach results that are connected to the most recent advances in theoretical physics. In each case, we list a number of open questions and we finally introduce a conjecture, on sliced spaces.
For the entire collection see [Zbl 1483.00042].
For the entire collection see [Zbl 1483.00042].
MSC:
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 53C22 | Geodesics in global differential geometry |
| 53-02 | Research exposition (monographs, survey articles) pertaining to differential geometry |
| 53Z05 | Applications of differential geometry to physics |
| 83C99 | General relativity |
| 54H99 | Connections of general topology with other structures, applications |
Keywords:
causal spacetimes; weighted manifold; causal order; Klein-Gordon equation; Lorentzian manifold; geodesically completeReferences:
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