Existence of steady gap solutions in rotating black hole magnetospheres

Under conditions prevailing in certain classes of compact astrophysical systems, the active magnetosphere of a rotating black hole becomes charge starved, giving rise to the formation of a spark gap in which plasma is continuously produced. The plasma production process is accompanied by curvature and inverse Compton emission of gamma rays in the GeV-TeV band, which may be detectable by current and future experiments. The properties of the gap emission have been studied recently using a fully general-relativistic model of a local steady gap. However, this model requires artificial adjustment of the electric current which is determined, in reality, by the global properties of the magnetosphere. In this paper we map the parameter regime in which steady gap solutions exist, using a steady-state gap model in Kerr geometry, and show that such solutions are allowed only under restrictive conditions that may not apply to most astrophysical systems. We further argue that even the allowed solutions are inconsistent with the global magnetospheric structure. We conclude that magnetospheric gaps are inherently intermittent, and point out that this may drastically change their emission properties.