2000/01/17 by Lars Andersson, Alan D. Rendall · 8 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Einstein #Geometry #Gravitational singularity #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Scalar (mathematics) #Scalar field #Singularity #Spacetime #Theoretical physics #gr-qc
paper · pdf · doi:10.1007/s002200100406
published as Commun.Math.Phys. 218 (2001) 479-511 · 38 pages
arxiv created 2000/01/17 · openalex publication_date 2001/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The most detailed existing proposal for the structure of spacetime singularities originates in the work of Belinskii, Khalatnikov and Lifshitz. We show rigorously the correctness of this proposal in the case of analytic solutions of the Einstein equations coupled to a scalar field or stiff fluid. More specifically, we prove the existence of a family of spacetimes depending on the same number of free functions as the general solution which have the asymptotics suggested by the Belinskii-Khalatnikov-Lifshitz proposal near their singularities. In these spacetimes a neighbourhood of the singularity can be covered by a Gaussian coordinate system in which the singularity is simultaneous and the evolution at different spatial points decouples.