  Supermassive black holes with masses of millions to billions of solar masses
are commonly found in the centers of galaxies. Astronomers seek to image jet
formation using radio interferometry, but still suffer from insufficient
angular resolution. An alternative method to resolve small structures is to
measure the time variability of their emission. Here, we report on gamma-ray
observations of the radio galaxy IC 310 obtained with the MAGIC telescopes
revealing variability with doubling time scales faster than 4.8 min. Causality
constrains the size of the emission region to be smaller than 20\% of the
gravitational radius of its central black hole. We suggest that the emission is
associated with pulsar-like particle acceleration by the electric field across
a magnetospheric gap at the base of the radio jet.
