  The observation of rapidly variable very high energy (VHE) gamma-rays from
non-aligned active galactic nuclei (AGNs), as reported from M87, proves
challenging for conventional theoretical acceleration and emission models. We
re-examine the centrifugal acceleration of particles by rotating jet
magnetospheres in the vicinity of accreting supermassive black hole systems and
analyze the energy constraints imposed for highly underluminous systems.
Applications are presented for conditions expected to be present in the radio
galaxy M87, assuming accretion onto the central black hole to occur in an
advection-dominated (ADAF) mode. We show that for a highly underluminous source
like M87, centrifugally accelerated electrons may reach Lorentz factors up to
$\gamma \sim (10^7-10^8)$, allowing inverse Compton (Thomson) upscattering of
sub-mm disk photons to the TeV regime. Upscattering of Comptonized disk photons
results in a flat TeV spectrum $L_{\nu} \propto \nu^{-\alpha_c}$ with spectral
index $\alpha_c \simeq 1.2$. The characteristic variability time scale is of
the order $r_{\rm L}/c$, which in the case of M87 corresponds to $\simeq 1.7$ d
for a typical light cylinder radius of $r_{\rm L} \simeq 5 r_{\rm s}$.
Centrifugal acceleration could thus provide a natural explanation for the
challenging VHE emission features in M87. Our results suggest that some
advection-dominated accreting (non-blazar) AGNs could well be observable VHE
emitting sources. (abridged)
