A note on the extendability of compact hypersurfaces to smooth Cauchy hypersurfaces
نویسنده
چکیده
Given a globally hyperbolic spacetime, the existence of a (smooth) spacelike Cauchy hypersurface S has been proven recently. Here, we prove that any acausal spacelike compact submanifold with boundary can be smoothly extended to a spacelike Cauchy hypersurface. Apart from the interest as a purely geometric question (applicable to the Cauchy problem in General Relativity), the result is motivated by applications to quantization.
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