Аннотации:
Construction of exact solutions of Einstein equations in General Relativity and its generalizations,
such as supergravities and string inspiredmodels in various dimensions is an important
problemof theoretical andmathematical physics. Herewe reviewone of themost efficient tools
which is applicable to large class of theories involvingmetric, scalar, vector and antisymmetric
form fields without higher-derivative terms, scalar potentials and cosmological constant. This
includes pure gravity in arbitrary dimensions, bosonic parts of supergravities, as well as many
non-supersymmetric gravity-matter systems. The method is based on dimensional reduction
of D-dimensional Einstein equations assuming the solutions to depend only on three independent
variables in away that the field equations reduce to those of the three-dimensional gravity
coupled scalar sigma-model. Typically this amounts to starting with the Einstein-Hilbert action
coupled to scalar-vector/antisymmetric formsector withMaxwell-dilaton type action and
restricting to field configurations admitting D−3 commuting Killing vectors. The corresponding
dimensional reduction is commonly referred as toroidal.