General Cosmological Solution of the Gravitational Equations with a Singularity in Time

1970/01/12 by I. M. Khalatnikov, E.M. LIFSHITZ · 4 citations
Physics and Astronomy · Mathematics · #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #Advanced Mathematical Theories and Applications #Singularity #Generality #Metric (unit) #Einstein #Physics #Gravitation #Degree (music) #Initial singularity #Gravitational singularity #Einstein equations #Classical mechanics #Theoretical physics #Mathematical physics #General relativity #Mathematics #Mathematical analysis #Universe #Quantum mechanics

paper · doi:10.1103/physrevlett.24.76

openalex publication_date 1970/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26

Abstract

A way is indicated to construct a general solution of the Einstein equations with a singularity, starting from a previously known solution of a lesser degree of generality. A qualitative description is given of the evolution of the metric in this general solution towards the singularity, which is of a complex, oscillatory nature.

Citations

• Occurrence of Singularities in Open Universes
• Gravitational Collapse and Space-Time Singularities
• The Cosmic Black-Body Radiation and the Existence of Singularities in Our Universe
• Investigations in relativistic cosmology
• Singularities in Closed Universes
• Mixmaster Universe

Cited by

• “All that Matter … in One Big Bang …”, &Other Cosmological Singularities
• Hyperbolic Kac–Moody algebras and chaos in Kaluza–Klein models
• Strongly coupled quantum field theory
• BKL singularity [wikipedia]