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The energy-momentum tensor for a particular matter component summarises itslocal energy-momentum distribution in terms of densities and current densities.We re-investigate under what conditions these local distributions can beintegrated to meaningful global quantities. This leads us directly to a classictheorem by Max von Laue concerning integrals of components of theenergy-momentum tensor, whose statement and proof we recall. In the first halfof this paper we do this within the realm of Special Relativity and in thetraditional mathematical language using components with respect to affinecharts, thereby focusing on the intended physical content and interpretation.In the second half we show how to do all this in a properdifferential-geometric fashion and on arbitrary space-time manifolds, this timefocusing on the group-theoretic and geometric hypotheses underlying theseresults. Based on this we give a proper geometric statement and proof of Laue'stheorem, which is shown to generalise from Minkowski space (which has themaximal number of isometries) to space-times with significantly lesssymmetries. This result, which seems to be new, not only generalises but alsoclarifies the geometric content and hypotheses of Laue's theorem. A series ofthree appendices lists our conventions and notation and summarises some of theconceptual and mathematical background needed in the main text.

Laue's Theorem Revisited: Energy-Momentum Tensors, Symmetries, and the Habitat of Globally Conserved Quantities