Evaluation of the Magnetic Field of Hot Jupiters within the Geometric Approach

We discuss theoretical and experimental foundations of the hypothesis on the origin of magnetic fields of the Earth and other astrophysical objects, proposed in the early 20th century by W. Sutherland, A. Einstein, and independently by Yu.S. Vladimirov. According to this hypothesis, the electric charges of the electron and proton slightly differ in magnitude, leading to the emergence of magnetic fields in rotating astrophysical objects. A theoretical justification of the Sutherland–Einstein hypothesis is presented in a simplified version of the 6D Kaluza–Klein theory, taking into account the consequences of the Kerr–Newman metric. The analysis shows that a fundamental dipole-type magnetic field should arise around any massive rotating body. However, in real astrophysical objects, such a field is largely screened and distorted by induced charges and currents. As an application, we consider the problem of determining the magnetic fields of hot Jupiters, since strong tidal effects in these giant exoplanets should result in approximately similar screening mechanisms.