A comment on the construction of the maximal globally hyperbolic Cauchy development. (English) Zbl 1288.83009
Summary: 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.{
©2013 American Institute of Physics}
©2013 American Institute of Physics}
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 70S20 | More general nonquantum field theories in mechanics of particles and systems |
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 53Z05 | Applications of differential geometry to physics |
| 03E25 | Axiom of choice and related propositions |
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