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Communications in Mathematical Physics

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

Self-similar spacetimes: Geometry and dynamics

  • Douglas M. Eardley
Article

Abstract

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.

Keywords

Neural Network Statistical Physic General Relativity Complex System Initial Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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