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

Abstract

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 $\mu =-\cos \theta$. By coordinate transformation, the form of the above equation can be given by $s_{,yy}+s_{,zz}+D(s(y,z),y,z)=0$. Based on the form, we prove finally that the Meissner effect is not possessed by a KBH-FFM with the condition where $d\omega /d{A}_{\varphi }⩽0$ and $H_{\varphi }(d{H}_{\varphi }/d{A}_{\varphi })⩾0$, here $A_{\varphi }$ is the $\varphi$ component of the vector potential $\vec{A}$, $\omega$ is the angular velocity of magnetic fields and $H_{\varphi }$ corresponds to twice the poloidal electric current.

References in corpus (4)

• Black Hole Magnetospheres
• The Black Hole Meissner Effect and Blandford-Znajek Jets
• Analytic properties of force-free jets in the Kerr spacetime -- II
• Black hole Meissner effect and entanglement

Cited by in corpus (4)

• Thermodynamics and phase transition in rotational Kiselev black hole
• Phase-Transition Theory of Kerr Black Holes in Electromagnetic Field
• Selected Chapters on Active Galactic Nuclei as Relativistic Systems
• Zooming in on the horizon when in its Meissner state