  This is our first study of the magnetic Rayleigh-Taylor instability at the
inner edge of an astrophysical disk around a central back hole. We derive the
equations governing small-amplitude oscillations in general relativistic ideal
magnetodydrodynamics and obtain a criterion for the onset of the instability.
We suggest that static disk configurations where magnetic field is held by the
disk material are unstable around a Schwarzschild black hole. On the other
hand, we find that such configurations are stabilized by the spacetime rotation
around a Kerr black hole. We obtain a crude estimate of the maximum amount of
poloidal magnetic flux that can be accumulated around the center, and suggest
that it is proportional to the black hole spin. Finally, we discuss the
astrophysical implications of our result for the theoretical and observational
estimations of the black hole jet power.
