Enveloping space of a globally hyperbolic conformally flat spacetime
Abstract
We prove that any simply-connected globally hyperbolic conformally flat spacetime V can be conformally embedded in a bigger conformally flat spacetime, called enveloping space of V , containing all the conformally flat Cauchy-extensions of V , in particular its C 0-maximal extension. As a result, we establish a new proof of the existence and the uniqueness of the C 0-maximal extension of a globally hyperbolic conformally flat spacetime. Furthermore, this approach allows us to prove that C 0-maximal extensions respect inclusion.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2023
- DOI:
- arXiv:
- arXiv:2311.17802
- Bibcode:
- 2023arXiv231117802S
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematical Physics