Abstract. It is shown that the usual characteristics of a black hole and of the physical fields produced by it obtain a unified geometrical meaning in the five-dimensional framework. Especidly, it is demonstrated that a solution for a rotating black hole with electric and scalar charges can he generated by a boost transformation of the fifth coordinate from the Kerr solution. (feladene, rotierende schwarze Lticher aus fiinf-dimensionalor SiehtInhaltsubersicht. Es wird gezeigt, wie die iiblichen Charakteristiken schw.wzer Ljcher iind der von ihnen erzeugten physikslischen Felder eine einheitliche geometrische Bedeutung im fiinfdimensionalen Formalismus erhalten. Speziell wird vorgefuhrt, daB man eine Losung fur ein rot,ierendea schwarzea Loch mit elektrischer und skalarer Ladung durch eine ,,b~ost"-Transformatsion der funften Koordinate aus der Ken-Losung erzeugen kann.Recently, the generalization of the standard EINSTEIN theory of gravitation to more than four dimensions by KALUZA [I] and KLEIN [ 2 ] is activly considered as a possible candidate for a unified field theory. The most important applications of this theories are early stages of the evolution of the Universe as well as compact astrophysical objects llke black holes. These cases are characterised by extremly strong fields and, therefore, specific properties of the more-dimensional theory may become significant. There is an extended literature on early cosmology in the framework of KALUZA-KLEIN theory ( 8 . e.g. [3-91). Concerning compact objects, in most of the papers (s. e.g. [ 10-151 the case of nonrotating black holes is considered.I n the present paper stationary axially symmet,ric five-dimensiod spaces are analysed, which correspond to regular four-dimensional rotating charged black holes.Suppose Mb to he a five-dimensional space-time covered by the metric GLin (-4, B = 0, 1, 2, 3; 5, sgii GAB = -+ + + +) providing a Killing vector field E.4(['),A EA = 2 f A~B E A 6 B = O ,(by ":" we denote the covariant derivative with respect to the 5-metric Gain). For 5 2 = fAtA we have the following relations:

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The authors consider general methods to solve the equations for Kaluza-Klein cosmological models by using the formal identity of these equations with those of a relativistic point particle in a scalar field. The formal scalar field is given by the phenomenological matter content of the cosmological model in dependence of the difference expansion factors. They find general solutions for one- and two-component matter and general properties of such models.

Multidimensional cosmological models with Einstein spaces are investigated. The cosmological constant and a homogeneous minimally coupled scalar field are considered as matter sources. The scalar field has a potential of general form depending on the scalar field as well as on the scale factors of the . The general condition of existence of the solutions with static internal spaces is obtained and applied to physically important cases.