The rapidly variable, very high-energy (VHE) gamma-ray emission from Active Galactic Nuclei (AGN) has been frequently associated with non-thermal processes occurring in the magnetospheres of their supermassive black holes. The present work aims to explore the adequacy of different gap-type (unscreened electric field) models to account for the observed characteristics. Based on a phenomenological description of the gap potential, we estimate the maximum extractable gap power L gap for different magnetospheric set-ups, and study its dependence on the accretion state of the source. L gap is found to be in general proportional to the Blandford-Znajek jet power L BZ and a sensitive function of gap sizeβ , where the power index β ≥ 1 is dependent on the respective gapsetup. The transparency of the black hole vicinity to VHE photons generally requires a radiatively inefficient accretion environment and thereby imposes constraints on possible accretion rates, and correspondingly on L BZ . Similarly, rapid variability, if observed, may allow to constrain the gap size h ∼ c∆t. Combining these constraints, we provide a general classification to assess the likelihood that the VHE gamma-ray emission observed from an AGN can be attributed to a magnetospheric origin. When applied to prominent candidate sources these considerations suggest that the variable (day-scale) VHE activity seen in the radio galaxy M87 could be compatible with a magnetospheric origin, while such an origin appears less likely for the (minute-scale) VHE activity in IC310.

The detection of rapidly variable gamma-ray emission in active galactic nuclei has generated renewed interest in magnetospheric particle acceleration and emission scenarios. In order to explore its potential, we study the possibility of steady gap acceleration around the null surface of a rotating black hole magnetosphere. We employ a simplified (1D) description along with the general relativistic expression of Gauss’s law, and we assume that the gap is embedded in the radiation field of a radiatively inefficient accretion flow. The model is used to derive expressions for the radial distribution of the parallel electric field component, the electron and positron charge density, the particle Lorentz factor, and the number density of γ-ray photons. We integrate the set of equations numerically, imposing suitable boundary conditions. The results show that the existence of a steady gap solution for a relative high value of the global current is in principle possible if charge injection of both species is allowed at the boundaries. We present gap solutions for different choices of the global current and the accretion rate. When put in context, our results suggest that the variable very-high-energy γ-ray emission in M87 could be compatible with a magnetospheric origin.