大样本恒星演化研究组知识库

The structure of the steady axisymmetric force-free magnetosphere of a Kerr black hole (BH) is governed by a second-order partial differential equation of Af depending on two "free" functions Omega(A(phi)) and I(A(phi)), where A(phi) is the f component of the vector potential of the electromagnetic field, O is the angular velocity of the magnetic field lines, and I is the poloidal electric current. In this paper, we investigate the solution uniqueness. Taking the asymptotically uniform field as an example, analytic studies imply that there are infinitely many solutions approaching the uniform field at infinity, while only a unique one is found in general relativistic magnetohydrodynamic simulations. To settle the disagreement, we reinvestigate the structure of the governing equation and numerically solve it with given constraint and boundary conditions. We find that the constraint condition (field lines smoothly crossing the light surface) and boundary conditions at the horizon and at infinity are connected via radiation conditions at horizon and at infinity, rather than being independent. With appropriate constraint and boundary conditions, we numerically solve the governing equation and find a unique solution. Contrary to naive expectations, our numerical solution yields a discontinuity in the angular velocity of the field lines and a current sheet along the last field line crossing the event horizon. We also briefly discuss the applicability of the perturbation approach to solving the governing equation.