  A detailed quantitative analysis of the transition process mediated by a
sphaleron type non-Abelian gauge field configuration in a static Einstein
universe is carried out. By examining spectra of the fluctuation operators and
applying the zeta function regularization scheme, a closed analytical
expression for the transition rate at the one-loop level is derived. This is a
unique example of an exact solution for a sphaleron model in $3+1$ spacetime
dimensions.
