2001/06/04 by B. K. Berger, Beverly K. Berger, Berger, Beverly K.
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0106009
17 pages, in Differential Equations and Mathematical Physics : Proceedings of an International Conference Held at the University of Alabama in Birmingham, ed. by R. Weikard, G. Weinstein (American Mathematical Society, 2000)
arxiv created 2001/06/04 · openalex publication_date 2001/06/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A combination of analytic and numerical methods has yielded a clear understanding of the approach to the singularity in spatially inhomogeneous cosmologies. Strong support is found for the longstanding claim by Belinskii, Khalatnikov, and Lifshitz that the collapse is dominated by local Kasner or Mixmaster behavior. The Method of Consistent Potentials is used to establish the consistency of asymptotic velocity term dominance (AVTD) (local Kasner behavior) in that no terms in Einstein's equations will grow exponentially when the VTD solution, obtained by neglecting all terms containing spatial derivatives, is substituted into the full equations. When the VTD solution is inconsistent, the exponential terms act dynamically as potentials either to drive the system into a consistent AVTD regime or to maintain an oscillatory approach to the singularity.