1994/11/15 by Nathalie Deruelle, N. Deruelle, D. Langlois +1 · 75 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Einstein #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Singularity #Spacetime #gr-qc
paper · pdf · doi:10.1103/physrevd.52.2007
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 52(4), 2007-2019 (American Physical Society) · 35 pages, revtex, no figures
arxiv created 1994/11/15 · openalex publication_date 1995/08/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the behavior of a very inhomogeneous spacetime near the singularity by using the recently developed long wavelength iteration scheme of Einstein's equations. Near the singularity, the local anisotropy cannot be neglected and we give the first order and third order solutions for any perfect fluid adiabatic index. We also clarify the links between a recently developed long wavelength iteration scheme of Einstein's equations, the Belinski-Khalatnikov-Lifschitz (BKL) general solution near a singularity and the anti-Newtonian scheme of Tomita's. We determine the regimes when the long wavelength or anti-Newtonian scheme is directly applicable and show how it can otherwise be implemented to yield the BKL oscillatory approach to a spacetime singularity.