Convex Functions and Spacetime Geometry

Details Convex Functions and Spacetime Geometry Convex Functions and Spacetime Geometry

2000-11-15

arxiv.org/abs/gr-qc/0011055v2

Class.Quant.Grav.18:4607-4628,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, latex, 7 figures, improved version. some claims removed, references added

Scientific paper

10.1088/0264-9381/18/21/314

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 $(M,g_{\mu \nu})$ or an initial data set $(\Sigma, h_{ij}, K_{ij})$ 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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