Introduces Lorentzian spaces as a weakening of Lorentzian length spaces and considers pointed Gromov-Hausdorff metrics, non-spacetime maximal examples, and canonical Cauchy development representatives.
A comment on the construction of the maximal globally hyperbolic Cauchy development
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abstract
Under mild assumptions, we remove all traces of the axiom of choice from the construction of the maximal globally hyperbolic Cauchy development in general relativity. The construction relies on the notion of direct union manifolds, which we review. The construction given is very general: any physical theory with a suitable geometric representation (in particular all classical fields), and such that a strong notion of "local existence and uniqueness" of solutions for the corresponding initial value problem is available, is amenable to the same treatment.
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math.DG 1years
2024 1verdicts
UNVERDICTED 1representative citing papers
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Maximality and Cauchy developments of Lorentzian length spaces
Introduces Lorentzian spaces as a weakening of Lorentzian length spaces and considers pointed Gromov-Hausdorff metrics, non-spacetime maximal examples, and canonical Cauchy development representatives.