Comparisons of the Lorentzian volumes between level hypersurfaces

The Lorentzian volume between compact subsets of level hypersurfaces of a globally hyperbolic space–time MM 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.