  We investigate the confinement-Coulomb phase transition in the
four-dimensional (4D) pure compact U(1) gauge theory on spherical lattices. The
action contains the Wilson coupling beta and the double charge coupling gamma.
The lattice is obtained from the 4D surface of the 5D cubic lattice by its
radial projection onto a 4D sphere, and made homogeneous by means of
appropriate weight factors for individual plaquette contributions to the
action. On such lattices the two-state signal, impeding the studies of this
theory on toroidal lattices, is absent for gamma le 0. Furthermore, here a
consistent finite-size scaling behavior of several bulk observables is found,
with the correlation length exponent nu in the range nu = 0.35 - 40. These
observables include Fisher zeros, specific-heat and cumulant extrema as well as
pseudocritical values of beta at fixed gamma. The most reliable determination
of nu by means of the Fisher zeros gives nu = 0.365(8). The phase transition at
gamma le 0 is thus very probably of 2nd order and belongs to the universality
class of a non-Gaussian fixed point.
