Diamond-Shaped Regions as Microcosmoi

Details Diamond-Shaped Regions as Microcosmoi Diamond-Shaped Regions as Microcosmoi

2010-10-25

arxiv.org/abs/1010.5032v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, no figures. Preliminary version, comments welcome

Scientific paper

We give a geometrically intrinsic construction of a global time function for relatively compact diamond-shaped regions in arbitrary spacetimes. In the case of Minkowski spacetime, the flow of diffeomorphisms associated to a suitably normalized gradient of this time function becomes the conformal isotropy subgroup of the diamond. In full generality, this time function is elegantly expressed in terms of the Lorentzian distance function, and it has an asymptotic behavior at large absolute times similar to the one in Minkowski spacetime.

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