Geroch, Robert Domain of dependence. (English) Zbl 0189.27602 J. Math. Phys. 11, No. 2, 437-449 (1970). Summary: The various properties of the domain of dependence (Cauchy development) which have been found particularly useful in the study of gravitational fields are reviewed. The basic techniques for constructing proofs and counterexamples are described. A new tool – the past and future volume functions – for treating certain global properties of space-times is introduced. These functions are used to establish two new theorems: (1) a necessary and sufficient condition that a space-time have a Cauchy surface is that it be globally hyperbolic; and (2) the existence of a Cauchy surface is a stable property of space-times. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 206 Documents MSC: 83Cxx General relativity Keywords:structure of matter PDFBibTeX XMLCite \textit{R. Geroch}, J. Math. Phys. 11, 437--449 (1970; Zbl 0189.27602) Full Text: DOI References: [1] DOI: 10.1103/PhysRevLett.14.57 · Zbl 0125.21206 · doi:10.1103/PhysRevLett.14.57 [2] DOI: 10.1098/rspa.1966.0221 · Zbl 0139.45803 · doi:10.1098/rspa.1966.0221 [3] DOI: 10.1098/rspa.1966.0255 · Zbl 0148.46504 · doi:10.1098/rspa.1966.0255 [4] DOI: 10.1098/rspa.1967.0164 · Zbl 0163.23903 · doi:10.1098/rspa.1967.0164 [5] DOI: 10.1017/S030500410004144X · doi:10.1017/S030500410004144X [6] DOI: 10.1063/1.1704019 · doi:10.1063/1.1704019 [7] DOI: 10.1063/1.1704019 · doi:10.1063/1.1704019 [8] DOI: 10.2307/1970071 · Zbl 0065.38802 · doi:10.2307/1970071 [9] DOI: 10.1063/1.1664507 · Zbl 0165.29402 · doi:10.1063/1.1664507 [10] DOI: 10.5802/aif.144 · Zbl 0188.54801 · doi:10.5802/aif.144 [11] DOI: 10.1063/1.1664507 · Zbl 0165.29402 · doi:10.1063/1.1664507 [12] DOI: 10.1063/1.1664507 · Zbl 0165.29402 · doi:10.1063/1.1664507 [13] DOI: 10.1098/rspa.1969.0018 · Zbl 0181.57303 · doi:10.1098/rspa.1969.0018 [14] DOI: 10.1007/BF01645486 · doi:10.1007/BF01645486 [15] DOI: 10.1063/1.1664507 · Zbl 0165.29402 · doi:10.1063/1.1664507 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.