On the theoretical possibility of the electromagnetic scalar potential wave spreading with an arbitrary velocity in vacuum

In this work we revisit the process of constructing wave equations for the scalar and vector potentials of an electromagnetic field, and show that a wave equation with an arbitrary velocity (including a velocity higher than the velocity of light in vacuum) for the scalar potential exists in the framework of classical electrodynamics. Some consequences of this fact are considered. It is shown (in the Appendix) at what point this work differs from works concerned of the problem of the gauge invariance in the classical electrodynamics.