[en] In order to investigate a physical connection between the quantum tunneling processes (vacuum-to vacuum transition or thermal radiation) of Yang-Mills and gravitational pseudoparticles, Tomimatsu compared several (especially, topological) properties of the Belavin and Schwarzschild solutions with each other in terms of their Euclidean metrics. The purpose of this letter is to point out that Tomimatsu's metric can be reduced further to that for the Friedmann universe with open 3-space at the radiation dominated stage. This also means that, via Tomimatsu's procedure relying on Carmeli's formalism for the general theory of relativity, the quantum creation of particles in the Belavin gauge field has an intimate connection with that in the early universe. (author)