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Convex Functions and Spacetime Geometry | | Gary W. Gibbons
; Akihiro Ishibashi
; | | Date: |
15 Nov 2000 | | Journal: | Class.Quant.Grav. 18 (2001) 4607-4628 | | Subject: | General Relativity and Quantum Cosmology; Differential Geometry | gr-qc hep-th math.DG | | 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 $(M,g_{mu
u})$ 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. | | Source: | arXiv, gr-qc/0011055 | | Services: | Forum | Review | PDF | Favorites | |
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