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arXiv · gr-qc/0011055

Convex Functions and Spacetime Geometry

Gary W. Gibbons·Akihiro Ishibashi
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Abstract

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{μν})$ or an initial data set $(Σ, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties of the spacetime geometry.

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Gary W. Gibbons, Akihiro Ishibashi. 2001-09-04. Convex Functions and Spacetime Geometry. https://doi.org/10.1088/0264-9381%2F18%2F21%2F314

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