2000/07/28 by Sijie Gao, Robert M. Wald · 6 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Causal sets #Causality (physics) #Computer science #Cosmology and Gravitation Theories #Energy condition #General relativity #Geodesic #Geodesics in general relativity #Geometric Analysis and Curvature Flows #Mathematical analysis #Mathematical physics #Mathematics #Null (SQL) #Physics #Pure mathematics #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Spacetime #Stationary spacetime #gr-qc
paper · pdf · doi:10.1088/0264-9381/17/24/305
published as Class.Quant.Grav. 17 (2000) 4999-5008 · 15 pages, 1 figure. Example of gauge perturbation changed/corrected. Two footnotes added and one footnote removed
arxiv created 2000/07/28 · openalex publication_date 2000/11/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically complete, then given any compact set K , there exists another compact set K ' such that for any p , q ∉ K ', if there exists a `fastest null geodesic', γ, between p and q , then γ cannot enter K . As an application of this theorem, we show that if, in addition, the spacetime is globally hyperbolic with a compact Cauchy surface, then any observer at sufficiently late times cannot have a particle horizon. The second theorem states that if a timelike conformal boundary can be attached to the spacetime such that the spacetime with boundary satisfies strong causality as well as a compactness condition, then any `fastest null geodesic' connecting two points on the boundary must lie entirely within the boundary. It follows from this theorem that generic perturbations of anti-de Sitter spacetime always produce a time delay relative to anti-de Sitter spacetime itself.