Effects of a gravitomagnetic field on pure superconductors

We report the results of an investigation of the effects of a pure superconductor on external gravitomagnetic and magnetic fields ${\mathrm{B}}_{g,0}$ and ${\mathbf{B}}_{0}$, respectively. We find that the internal fields are given by $\mathrm{B}(z)\ensuremath{\approx}\ensuremath{-}(\frac{{m}^{2}{\ensuremath{\mu}}_{g}}{{q}^{2}\ensuremath{\mu}}){\mathrm{B}}_{0}\ensuremath{-}(\frac{m}{q}){\mathrm{B}}_{g,0}$, ${\mathrm{B}}_{g}(z)\ensuremath{\approx}{\mathrm{B}}_{g,0}+(\frac{{\ensuremath{\mu}}_{g}m}{\mathrm{qu}}){\mathrm{B}}_{0}$, where ${\ensuremath{\mu}}_{g}$ and $\ensuremath{\mu}$ are the gravitomagnetic and magnetic permeabilities of the superconductor. These results show that a small residual uniform magnetic field will pervade the superconductor and that the external fields mutually "induce" additional small internal perturbation fields. The sum of the fields $\mathrm{B}+(\frac{m}{q}){\mathrm{B}}_{g}$ falls exponentially to zero over a characteristic distance $\ensuremath{\lambda}$, which is consistent with previous findings that $\mathrm{B}+(\frac{m}{q}){\mathrm{B}}_{g}=0$ inside a pure superconductor.