Self-similar spacetimes: Geometry and dynamics

Details Self-similar spacetimes: Geometry and dynamics Self-similar spacetimes: Geometry and dynamics

Dec 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cmaph..37..287e&link_type=abstract

Communications in Mathematical Physics, Volume 37, Issue 4, pp.287-309

Mathematics

Mathematical Physics

119

Scientific paper

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.

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