Convex Functions and Spacetime Geometry
Differential Geometry
2017-02-21 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
math.MP
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 or an initial data set 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.
Cite
@article{arxiv.1702.05584,
title = {Convex Functions and Spacetime Geometry},
author = {Gary W. Gibbons and Akihiro Ishibashi},
journal= {arXiv preprint arXiv:1702.05584},
year = {2017}
}
Comments
In the light of recent renewed interest in this topic (see arxiv: 1510.04228 and 1702.02652) we are submitting this brief summary of our old results presented by A.I. at the International Workshop: Frontiers of Cosmology and Gravitation held in Kyoto in 2001.and published in the proceedings. See also arXiv:gr-qc/0011055