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EXACT SOLUTIONS IN
MULTIDIMENSIONAL GRAVITY WITH
P–BRANES AND PPN PARAMETERS
V. D. Ivashchuk
Center for Gravitation and Fundamental Metrology, VNIIMS,
3–1 M. Ulyanovoy Str., Moscow, 117313, Russia
Institute of Gravitation and Cosmology, Peoples’ Friendship University,
6 Miklukho–Maklaya St., Moscow 117198, Russia.
V. N. Melnikov*
Center for Gravitation and Fundamental Metrology, VNIIMS,
3–1 M. Ulyanovoy Str., Moscow, 117313, Russia
Institute of Gravitation and Cosmology, Peoples’ Friendship University,
6 Miklukho–Maklaya St., Moscow 117198, Russia.
Abstract
Multidimensional gravitational model containing several dilatonic
scalar fields and antisymmetric forms is considered. The manifold is
chosen in the form where are Einstein
spaces The sigma-model representation for p–branes ansatz
and exact solutions in the model are given (e.g. solutions depending on
harmonic function, spherically symmetric ones and black holes). PPN
parameters for 4–dimensional section of the metric are also presented.
Keywords: Multidimensional gravity, p–branes, exact solutions.
1. INTRODUCTION
More than 30 years passed after the pioneering paper [1] of Dietrich
Kramer on spherically symmetric solution in 5–dimensional model (suggested
by E. Schmutzer). Later this solution was rediscovered by several
* Visiting Professor at Depto.de Fisica, CINVESTAV, A.P.14–740, Mexico 07000, D.F.
Exact Solutions and Scalar Fields in Gravity: Recent Developments
Edited by Macias et al., Kluwer Academic/Plenum Publishers, New York, 2001 123