Aspectos gerais da teoria de Kaluza-Klein e mecanismo de compactificação

Abstract

In this work we will explore the theory of Kaluza-Klein, that proposes to unify the electromagnetism with the gravitation in one classical approach through the addition of one extra dimension (space type), thus obtaining one composed variety by 4 spatial dimensions and 1 time dimension. We will see how to obtain Einstein’s equations in this model and ,thereby, explain their consequences and restrictions when we do one dimensional reduction in order to rescue the known equations in 4 dimensions. We will analyse the compaction of this extra dimension and we will use one mechanism of spontaneous compaction in the case where we will have more than one extra dimension in the theory, this mechanism is known as flux compaction. This mechanism of compaction is done through the introduction of a tensor totally antisymmetric in the Eistein’s equations in 5 dimensions. Finally, we will approach the Kaluza-Klein theory using the formalism of differential forms, showing that it is a powerful tool in this study once that its algebra allowed us to obtain the same results in less time.