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
MINGUZZI, ETTORE
2016-01-01
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.File in questo prodotto:
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