Slowly balding black holes
Abstract
The ``no-hair'' theorem, a key result in general relativity, states that an isolated black hole is defined by only three parameters: mass, angular momentum, and electric charge; this asymptotic state is reached on a light-crossing time scale. We find that the no-hair theorem is not formally applicable for black holes formed from the collapse of a rotating neutron star. Rotating neutron stars can self-produce particles via vacuum breakdown forming a highly conducting plasma magnetosphere such that magnetic field lines are effectively ``frozen in'' the star both before and during collapse. In the limit of no resistivity, this introduces a topological constraint which prohibits the magnetic field from sliding off the newly-formed event horizon. As a result, during collapse of a neutron star into a black hole, the latter conserves the number of magnetic flux tubes ${N}_{B}=e{\ensuremath{\Phi}}_{\ensuremath{\infty}}/(\ensuremath{\pi}c\ensuremath{\hbar})$, where ${\ensuremath{\Phi}}_{\ensuremath{\infty}}\ensuremath{\approx}2{\ensuremath{\pi}}^{2}{B}_{\mathrm{NS}}{R}_{\mathrm{NS}}^{3}/({P}_{\mathrm{NS}}c)$ is the initial magnetic flux through the hemispheres of the progenitor and out to infinity. We test this theoretical result via 3-dimensional general relativistic plasma simulations of rotating black holes that start with a neutron star dipole magnetic field with no currents initially present outside the event horizon. The black hole's magnetosphere subsequently relaxes to the split-monopole magnetic field geometry with self-generated currents outside the event horizon. The dissipation of the resulting equatorial current sheet leads to a slow loss of the anchored flux tubes, a process that balds the black hole on long resistive time scales rather than the short light-crossing time scales expected from the vacuum no-hair theorem.