Time Evolution as a Gauge Transformation: x⁵-dependent Cosmological Solution in 5d Kaluza-Klein Theory

We discuss a new feature of the 5d Kaluza-Klein cosmology. For that purpose, we obtain the simplest x^5-dependent solution which, in the reduced description, is associated with a radiation-dominated Robertson-Walker universe, and also can be regarded as an extension of the Schwarzschild solution. This solution enables us to deduce an important result that an evolving universe is related with a static universe by the gauge transformation, i.e., they are gauge equivalent. This means that having a different universe simply corresponds to choosing a different gauge