Selfsimilar space-times: Geometry and dynamics

Dec, 1973
23 pages
Published in:
  • Commun.Math.Phys. 37 (1974) 287-309

Citations per year

19771989200120132025012345
Abstract: (Springer)
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.