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 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 $N_B = e \Phi_\infty /(\pi c \hbar)$, where $\Phi_\infty \approx 2 \pi^2 B_{NS} R_{NS}^3 /(P_{\rm NS} c)$ is the initial magnetic flux through the hemispheres of the progenitor and out to infinity. We test this theoretical result via three-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.