Exact solutions and the effective equation of state in Kaluza–Klein theory

A generalization of the standard class of solutions in the Kaluza–Klein (4+1) gravity, wherein the spherically symmetric metric depends not only on the radius but also on the extra coordinate, is considered. Two new classes of exact solutions of the empty Kaluza–Klein field equations are given. However, it is known that apparently empty solutions of the (4+1) Kaluza–Klein equations can be interpreted as solutions with effective matter properties of the (3+1) Einstein equations. The physical importance of the new solutions is that in this approach the dependency on the extra coordinate allows us to obtain more general equations of state than before, including ones for radiation, dust, vacuum, and stiff matter.