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 size h , i.e . L _ { gap } \sim L _ { BZ } ( h / r _ { g } ) ^ { \beta } , where the power index \beta \geq 1 is dependent on the respective gap-setup .
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 \sim c \Delta 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 .