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Under conditions prevailing in certain classes of compact astrophysicalsystems, the active magnetosphere of a rotating black hole becomescharge-starved, giving rise to formation of a spark gap in which plasma iscontinuously produced. The plasma production process is accompanied bycurvature and inverse Compton emission of gamma rays in the GeV-TeV band, thatmay be detectable by current and future experiments. The properties of the gapemission have been studied recently using a fully general relativistic model ofa local steady gap. However, this model requires artificial adjustment of theelectric current which is determined, in reality, by the global properties ofthe magnetosphere. In this paper we map the parameter regime in which steadygap solutions exist, using a steady-state gap model in Kerr geometry, and showthat such solutions are allowed only under restrictive conditions that may notapply to most astrophysical systems. We further argue that even the allowedsolutions are inconsistent with the global magnetospheric structure. Weconclude that magnetospheric gaps are inherently intermittent, and point outthat this may drastically change their emission properties.

Existence of steady gap solutions in rotating black hole magnetospheres