Communications in Mathematical Physics

, Volume 218, Issue 3, pp 479–511 | Cite as

Quiescent Cosmological Singularities

  • Lars Andersson
  • Alan D. Rendall


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.


Coordinate System General Solution Scalar Field Einstein Equation Spatial Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Lars Andersson
    • 1
  • Alan D. Rendall
    • 2
  1. 1.Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden.¶E-mail:larsa@math.kth.seSE
  2. 2.Max–Planck–Institut für Gravitationsphysik, Am Mühlenberg 1, 14424 Golm, Germany.¶E-mail: rendall@aei-potsdam.mpg.deDE

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