Upper and lower bounds for the volume of a compact spacelike hypersurface in a generalized Robertson-Walker spacetime (Q2874228)

Generalized Robertson-Walker (GRW) spacetimes have been introduced by \textit{L. J. Alías} et al. [Gen. Relativ. Gravitation 27, No. 1, 71--84 (1995; Zbl 0908.53034)]. The authors of the paper under review obtain upper and lower bounds for the volume of a compact spacelike hypersurface in a GRW spacetime, in terms of the volume of the fiber, the hyperbolic angle function, and the warping function. Also, it is proved that both bounds are attained, if and only if, the hypersurface is a spacelike slice of a proper GRW spacetime. As consequences of these results, the authors present some geometrical applications with physical interpretations.