Exact solutions in gravity with a sigma model source

Abstract

We consider a D-dimensional model of gravity with non-linear "scalar fields" as a matter source. The model is defined on the product manifold M, which contains n Einstein factor spaces. General cosmological type solutions to the field equations are obtained when n-1 factor spaces are Ricci-flat, e.g. when one space M_1 of dimension d_1 > 1 has nonzero scalar curvature. The solutions are defined up to solutions to geodesic equations corresponding to a sigma model target space. Several examples of sigma models are presented. A subclass of spherically-symmetric solutions is studied and a restricted version of "no-hair theorem" for black holes is proved. For the case d_1 =2 a subclass of latent soliton solutions is singled out.

22 pages, Latex, several phrases and 4 refs. are addes, few typos are eliminated

References in corpus (3)

• The Abnormally Weighting Energy Hypothesis: the Missing Link between Dark Matter and Dark Energy
• De-Sitter nonlinear sigma model and accelerating universe
• Spherically-symmetric solutions with a chain of n internal Ricci-flat spaces

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