A note on spacelike and timelike compactness

作者：Sanders Ko^*

来源：Classical and Quantum Gravity, 2013, 30(11): 115014.

DOI：10.1088/0264-9381/30/11/115014

When studying the causal propagation of a field phi in a globally hyperbolic spacetime M, one often wants to express the physical intuition that phi has compact support in spacelike directions, or that its support is a spacelike compact set. We compare a number of logically distinct formulations of this idea, and of the complementary idea of timelike compactness, and we clarify their interrelations. E.g., a closed set A subset of M has a compact intersection with all Cauchy surfaces if and only if A subset of J (K) for some compact set K. (However, it does not suffice to consider only those Cauchy surfaces that partake in a given foliation of M.) Similarly, a closed set A subset of M is contained in a region of the form J(+) (Sigma(-)) boolean AND J(-) (Sigma(+)) for two Cauchy surfaces Sigma(+/-) if and only if the intersection of A with J (K) is compact for all compact K. We also treat advanced, retarded and future and past compact sets in a similar way.

• 出版日期2013-6-7