A simple proof (based on results in Chruściel et al 2015 Ann. Henri Poincaré arXiv:1301.2909) is given that every globally hyperbolic spacetime admits a smooth Cauchy steep time function. This result is useful in order to show that globally hyperbolic spacetimes can be isometrically embedded in Minkowski spacetimes and that they split as a product. The proof is based on a recent result on the differentiability of Geroch's volume functions.
On the existence of smooth Cauchy steep time functions / E. Minguzzi. - In: CLASSICAL AND QUANTUM GRAVITY. - ISSN 0264-9381. - STAMPA. - 33:(2016), pp. 115001-1-115001-4. [10.1088/0264-9381/33/11/115001]
On the existence of smooth Cauchy steep time functions
MINGUZZI, ETTORE
2016
Abstract
A simple proof (based on results in Chruściel et al 2015 Ann. Henri Poincaré arXiv:1301.2909) is given that every globally hyperbolic spacetime admits a smooth Cauchy steep time function. This result is useful in order to show that globally hyperbolic spacetimes can be isometrically embedded in Minkowski spacetimes and that they split as a product. The proof is based on a recent result on the differentiability of Geroch's volume functions.
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