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Global spacetime similarity. (English) Zbl 1409.53058

Taking into account mathematical viewpoint we can consider many different topologies on the space of Lorentz metrics on a fixed manifold. Not all mathematical properties are physically meaningful. Among others, each topology captures a slightly different type of similarity. There are two classes of topologies most often placed on the space of Lorentz metrics: the compact-open and open (Whitney) topologies. The author considers properties of these standard classes and shows that neither of them correctly capture a notion of global spacetime similarity. Next the author constructs the global topology on the Lorentz metrics, which divides them into an infinite number of uniform components. This topology succeeds in capturing a notion of global spacetime similarity. He also describes an application of the global topologies to our understanding of the stability and genericity of global properties of spacetimes. Finally, the author presents some open questions concerning invariant and geometrical properties of the global topologies.

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
58D17 Manifolds of metrics (especially Riemannian)

Citations:

Zbl 0339.53038
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References:

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