Schmidt boundaries of foliated space-times

• Published in: Classical and quantum gravity Vol. 31; no. 20; pp. 205012 - 28
• Main Authors: Barletta, Elisabetta, Dragomir, Sorin, Magliaro, Marco
• Format: Journal Article
• Language: English
• Published: IOP Publishing 21.10.2014
• Subjects: adapted connection; Boundaries; boundary; bundle-like metric; Bundling; completion; Construction; Fields (mathematics); foliation; Killing; Manifolds (mathematics); Quantum gravity; Schwarzschild metric; Tangents
• ISSN: 0264-9381; 1361-6382
• DOI: 10.1088/0264-9381/31/20/205012

For every -dimensional foliated Lorentzian manifold , where is a codimension q space-like foliation, we build its Q-completion and Q-boundary . These are analogs, within transverse Lorentzian geometry of foliated manifolds, to the b-completion and b-boundary (due to (Schmidt 1971 Gen. Relativ. Gravit. 1 269-80)). The bundle morphism (mapping the -component of the Levi-Civita connection 1-form of into the unique torsion-free adapted connection on the bundle of Lorentzian transverse orthonormal frames) is shown to induce a surjective continuous map of the adapted boundary ( ) of onto its Q-boundary. Map is used to characterize as the set of end points , in the topology of , of all Q-incomplete curves . As an application we determine a class of b-boundary points, where , g is Schwartzschildʼs metric, and is the codimension two foliation tangent to the Killing vector fields and .