Omniscient foliations and the geometry of cosmological spacetimes

We identify certain general geometric conditions on a foliation of a spacetime ( M ,  g ) by timelike curves that will impede the existence of null geodesic lines, especially if ( M ,  g ) possesses a compact Cauchy hypersurface. The absence of such lines, in turn, yields well-known restrictions on...

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Bibliographic Details
Published inGeneral relativity and gravitation Vol. 54; no. 11
Main Authors Costa e Silva, Ivan P., Flores, José L., Herrera, Jónatan
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2022
Springer Nature B.V
Subjects
Astronomy
Astrophysics and Cosmology
Classical and Quantum Gravitation
Differential Geometry
Geodesic lines
Gravity
Hyperspaces
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Rescaling
Research Article
Theoretical
Rigidity of geodesic incompleteness
Foliations
Lorentzian Geometry
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Summary:We identify certain general geometric conditions on a foliation of a spacetime ( M ,  g ) by timelike curves that will impede the existence of null geodesic lines, especially if ( M ,  g ) possesses a compact Cauchy hypersurface. The absence of such lines, in turn, yields well-known restrictions on the geometry of cosmological spacetimes, in the context of Bartnik’s splitting conjecture. Since the (non)existence of null lines is actually a conformally invariant property, such conditions only need to apply for some suitable conformal rescaling of g .
ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-022-03033-z