Gravitationally induced electromagnetism at the Compton scale

It is shown that Einstein gravity tends to modify the electric and magnetic fields appreciably at length scales of the order of the Compton wavelength. At that scale the gravitational field becomes spin dominated rather than mass dominated. The gravitational field couples to the electromagnetic field via the Einstein Maxwell equations which in the simplest model (Kerr Newman) causes the electrostatic field of charged spinning particles to acquire an oblate structure relative to the spin direction. For electrons and protons, the Coulomb field is therefore likely to be modified by general relativity at the Compton scale. In the Kerr Newman model, the magnetic dipole is known to correspond to the Dirac g-factor, g = 2. Also, the electric dipole moment vanishes, in agreement with current experimental limits for the electron. Quantitatively, the classical Einstein Maxwell field represented by the Kerr Newman solution models the magnetic and electric dipoles of the electron to an accuracy of about one part in 10^-3 or better taking into account also the anomalous magnetic moment. Going to the next multipole order, one finds for the Kerr Newman model that the first non-vanishing higher multipole is the electric quadrupole moment which acquires the value -124 b for the electron. Any non-zero value of the electric quadrupole moment for the electron or the proton would be a clear sign of curvature due to the implied violation of rotation invariance. There is also a possible spherical modification of the Coulomb force proportional to r^-4. However, the size of this effect is well below current experimental limits. The corrections to the hydrogen spectrum are expected to be small but possibly detectable.