Magnetic Hair and Reconnection in Black Hole Magnetospheres

The no-hair theorem of general relativity states that isolated black holes are characterized by three parameters: mass, spin, and charge. In this Letter we consider Kerr black holes endowed with highly magnetized plasma-filled magnetospheres. Using general relativistic kinetic plasma and resistive magnetohydrodynamics simulations, we show that a dipole magnetic field on the event horizon opens into a split monopole and reconnects in a plasmoid-unstable current sheet. The no-hair theorem is satisfied, in the sense that all components of the stress-energy tensor decay exponentially in time. We measure the decay time of magnetic flux on the event horizon for plasmoid-dominated reconnection in collisionless and collisional plasma. The reconnecting magnetosphere should be a powerful source of hard x-ray emission when the magnetic field is strong.

Figure 1

Reconnecting magnetosphere in the FIDO frame (GRPIC1) at $t=100$ $r_g/c$. Green curves show poloidal magnetic flux surfaces, and white curves show the boundary of the ergosphere. The black circle is the interior of the BH event horizon. Left: color shows radial and $\theta$ components of the bulk plasma three-velocity in the orthonormal tetrad basis. The grey dashed curve indicates the stagnation surface defined by $⟨v^r⟩=0$. Right: azimuthal component of the auxiliary field $\mathit{H}$.

Figure 2

Different realizations of the reconnecting magnetosphere in the FIDO frame. Color shows the cold plasma magnetization $\sigma$. Top: GRPIC1 at $t=100$ $r_g/c$, $\sigma =B^2/(4\pi mn{c}^2)$. Bottom: GRRMHD1 at $t=311$ $r_g/c$, $\sigma =B^2/(4\pi \rho c^2)$. The GRPIC simulation (top) displays larger plasmoids than GRRMHD (bottom) due to the faster reconnection rate of collisionless plasma.

Figure 3

Flux on the event horizon vs time for vacuum (power law decay), collisional MHD plasma (exponential decay), and collisionless plasma (faster exponential decay).

Figure 4

Reconnecting magnetosphere in 3D (GRRMHD2) at $t=118$ $r_g/c$. Left: volume rendering shows $\sigma =B^2/(4\pi \rho c^2)$, green tubes are magnetic field lines which penetrate the event horizon, red tubes are magnetic field lines which are reconnecting in the current sheet. Right: 2D slice of GRRMHD2 in the $\varphi =0$ half-plane. Color shows $\sigma$, green curves are magnetic field lines in the $\varphi =0$ half-plane. The picture highlights the nonaxisymmetric nature of reconnection in 3D, yet still displays similar fundamental structures—$X$ points (inset 1), and helical winding of magnetic field lines in plasmoids (flux ropes) (inset 2).