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Elsevier, Differential Geometry and its Applications, 2(16), p. 121-131, 2002

DOI: 10.1016/s0926-2245(02)00062-1

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A note on the boundary of a static Lorentzian manifold

Journal article published in 2002 by Rossella Bartolo, Anna Germinario, Miguel Sánchez ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

In this paper we characterize the convexity of the boundary ∂S of a static (standard) Lorentzian manifold S in terms of Jacobi metrics. From this result, we also obtain: (1) a characterization of the convexity of ∂S computable from its "spacelike" part, (2) the equivalence between the variational and geometrical definitions of convexity for ∂S, and (3) a very precise result on existence of geodesics joining a point and a line on S.  2002 Elsevier Science B.V. All rights reserved.