Exact power law metrics in cosmology

Details Exact power law metrics in cosmology Exact power law metrics in cosmology

May 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cqgra...3..281j&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 3, May 1, 1986, p. 281-309. Research supported by Stockholms Universitet, U

Mathematics

20

Cosmology, Einstein Equations, Gravitational Fields, Space-Time Functions, Differential Equations, Equations Of State, Lie Groups, Matrices (Mathematics), Orthogonality

Scientific paper

Spatially homogeneous and nonexceptional spatially self-similar spacetime metrics which are 'exact power law metrics' are defined, explicitly parametrized and shown to have fixed conformal 3-geometry in the natural slicing of the spacetime by the orbits of the symmetry group and to admit a homothetic Killing vector field not tangent to that slicing. In fact the exact power law metrics are exactly those spatially homogeneous and spatially self-similar metrics which admit a homothetic Killing vector field not tangent to the spacelike orbits of the homogeneity or self-similarity group. Such metrics arise as 'singular point solutions' of gravitational field equations when formulated as a certain system of first-order ordinary differential equations. These special exact solutions play an important role in the qualitative behavior of the general solution of a given set of field equations and sources with these symmetries.

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