RUSSIAN GRAVITATIONAL SOCIETY INSTITUTE OF METROLOGICAL SERVICE CENTER OF GRAVITATION AND FUNDAMENTAL METROLOGY RGS-VNIIMS-003-96 hep-th/9612054 MULTIDIMENSIONAL GRAVITY WITH EINSTEIN INTERNAL SPACES
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چکیده
A multidimensional gravitational model on the manifold M = M0 × ∏ n i=1 Mi , where Mi are Einstein spaces (i ≥ 1), is studied. For N0 = dimM0 > 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 = R N0 , N0 = 3, 4, 6 (and the total dimension D = dimM = 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 R0 . Submitted to Gravitation and Cosmology Moscow 1996 ] e-mail: [email protected] On leave from Centre for Gravitation and Fundamental Metrology, VNIIMS, 3–1 M. Ulyanovoy Str., Moscow 117313, Russia Multidimensional Gravity with Einstein Internal Spaces 1
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RUSSIAN GRAVITATIONAL SOCIETY INSTITUTE OF METROLOGICAL SERVICE CENTER OF GRAVITATION AND FUNDAMENTAL METROLOGY RGS-VNIIMS-004-96 hep-th/9612089 INTERSECTING P-BRANE SOLUTIONS IN MULTIDIMENSIONAL GRAVITY AND M-THEORY
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