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 ${\mathrm{B}}_{g,0\mathrm{}}$ and ${\mathbf{B}}_0$, respectively. We find that the internal fields are given by $\mathrm{B}\mathrm{}\left(z\right)\mathrm{}\approx -\left(\frac{m^2{\mu }_g}{q^2\mu }\right){\mathrm{B}}_0-\left(\frac{m}{q}\right){\mathrm{B}}_{g,0\mathrm{}}$, ${\mathrm{B}}_g\mathrm{}\left(z\right)\mathrm{}\approx {\mathrm{B}}_{g,0\mathrm{}}+\left(\frac{{\mu }_{g}m}{\mathrm{qu}}\right){\mathrm{B}}_0$, where ${\mu }_g$ and $\mu$ 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 $\mathrm{B}+\left(\frac{m}{q}\right){\mathrm{B}}_g$ falls exponentially to zero over a characteristic distance $\lambda$, which is consistent with previous findings that $\mathrm{B}+\left(\frac{m}{q}\right){\mathrm{B}}_g=0\mathrm{}$ inside a pure superconductor.