On the Universality of the Split Monopole Black Hole Magnetosphere

Black holes (BHs) can acquire magnetic flux from their progenitor, through merger with a magnetized star, or via prolonged accretion. We study the evolution of BH magnetospheres using axisymmetric general relativistic magnetohydrodynamic simulations. We show that all initial magnetic field configurations, regardless of complexity, ultimately evolve into a split monopole. The magnetospheric evolution proceeds in two phases. In the first phase, pressure equilibrates on fast Alfvénic timescales (∼60 gravitational light-crossing times), and the flux on the BH event horizon drops sharply. The second phase proceeds in pressure balance, in which the magnetic flux decays via magnetic reconnection in current sheets, governing the dynamics on slower resistive timescales. We present an analytic model for the second phase, quantitatively describing the evolution of flux and current sheet dynamics. Additionally, we show that in the split monopole configuration, magnetic flux decays exponentially, with higher BH spin leading to slower decay. Our results enable a quantitative prediction of the timescales and spatial structure of these evolving magnetospheres, essential for understanding electromagnetic counterparts to gravitational wave events and reconnection-powered flares from accreting BHs.