Communications in Mathematical Physics

, Volume 37, Issue 4, pp 287–309 | Cite as

Self-similar spacetimes: Geometry and dynamics

  • Douglas M. Eardley


The nature and uses of self-similarity in general relativity are discussed. A spacetime may be self-similar (homothetic) along surfaces of any dimensionality, from 1 to 4. A geometric construction is given for all self-similar spacetimes. As an important special case, the “spatially self-similar cosmological models” are introduced, and their dynamical properties are studied in some detail: The initial-value problem is posed, the ADM formulation is established (when applicable), and it is shown that the evolution equations preserve a self-similarity of initial data. The existence of a conserved quantity is deduced from self-similarity. Possible applications to cosmology and singularities are mentioned.


Neural Network Statistical Physic General Relativity Complex System Initial Data 
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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Douglas M. Eardley
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

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