A mathematical form of force-free magnetosphere equation around Kerr black holes and its application to Meissner effect

Based on the Lagrangian of the steady axisymmetric force-free magnetosphere (FFM) equation around Kerr black holes (KBHs), we find that the FFM equation can be rewritten in a new form as f ,(rr)/(1 - mu(2)) + f, (mu mu)/ Delta + K(f(r, mu), r, mu) = 0, where mu = -cos theta. With coordinate transformation, the above equation can be given as s, yy + s,(zz)+ D(s(y, z), y, z) = 0. Using this form, we prove that the Meissner effect is not possessed by a KBH-FFM with the condition d omega/dA(phi) <= 0 and H-phi (dH(phi)/dA(phi)) >= 0, here A(phi) is the phi component of the vector potential (A) over right arrow, omega is the angular velocity of magnetic fields and H-phi corresponds to twice the poloidal electric current. (C) 2016 Published by Elsevier B.V. This is an open access article under the CC BY license.