Jp. Deleon et Ps. Wesson, EXACT-SOLUTIONS AND THE EFFECTIVE EQUATION OF STATE IN KALUZA-KLEIN THEORY, Journal of mathematical physics, 34(9), 1993, pp. 4080-4092
A generalization of the standard class of solutions in the Kaluza-Klei
n (4 + 1) gravity, wherein the spherically symmetric metric depends no
t only on the radius but also on the extra coordinate, is considered.
Two new classes of exact solutions of the empty Kaluza-Klein field equ
ations 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. T
he physical importance of the new solutions is that in this approach t
he dependency on the extra coordinate allows us to obtain more general
equations of state than before, including ones for radiation, dust, v
acuum, and stiff matter.