Schmidt boundaries of foliated space-times
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. Gravi...
Saved in:
Published in | Classical and quantum gravity Vol. 31; no. 20; pp. 205012 - 28 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
IOP Publishing
21.10.2014
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | 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 . |
---|---|
Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 0264-9381 1361-6382 |
DOI: | 10.1088/0264-9381/31/20/205012 |