1996/12/05 by V. D. Ivashchuk, V. N. Melnikov
Physics and Astronomy · #hep-th #gr-qc
published as Grav.Cosmol. 2 (1996) 211-220 · 10 pages, LaTex
arxiv created 1996/12/05 · arxiv updated 2009/11/30
A multidimensional gravitational model on the manifold M = M0 × ∏i=1n Mi, where Mi are Einstein spaces (i ≥ 1), is studied. For N0 = dim M0 > 2 the σ model representation is considered and it is shown that the corresponding Euclidean Toda-like system does not satisfy the Adler-van-Moerbeke criterion. For M0 = RN0, N0 = 3, 4, 6 (and the total dimension D = dim M = 11, 10, 11, respectively) nonsingular spherically symmetric solutions to vacuum Einstein equations are obtained and their generalizations to arbitrary signatures are considered. It is proved that for a non-Euclidean signature the Riemann tensor squared of the solutions diverges on certain hypersurfaces in RN0.