Comparisons of the Lorentzian volumes between level hypersurfaces

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Abstract

The Lorentzian volume between compact subsets of level hypersurfaces of a globally hyperbolic space–time M is compared with that of the model space M̄ of either the space–time of constant curvature or a Robertson–Walker space–time by the comparison theorem of the Riccati equations including the equality of the Lorentzian volume comparison.

MSC

53C50

Keywords

Volume comparison
Globally hyperbolic space–time
Lorentzian warped product
Riccati equation

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