Abstract

Due to the complexity of the Einstein equations the general solution to these equations remains unknown. Currently there exist quite a few special solutions, which were obtained by assuming some symmetries of the solution, which allows one to reduce the complexity of these equations. That is one of the reasons why any exact solution is important. It may shed some light on the general problem.
There is also demand from string theories for a special type of solutions - compactified solu- tions. String theories use more than 4 dimensions and in order for these theories to make physical sense the extra dimensions must be compactified. Therefore the search for the compactified analogs of the known solutions became an important task.
The well known and widely used in physics non compactified solutions are the Schwarzschild [15] and Kerr [11] solutions, which are discussed in detail in Chapter 2 of this thesis. Chapter 2 also provides a description of the compactified analog of the Schwarzschild solution obtained independently by Korotkin and Nicolai [12] and by Myers [14]. However the compactified analog of the Kerr solution remains unknown.
In Chapter 3 the asymptotic behaviour of the compactified analog of the Kerr solution is inves- tigated. Two possible ways of solving this problem are discussed.