The accretion of matter onto a massive black hole is believed to feed the
relativistic plasma jets found in many active galactic nuclei (AGN).
Although some AGN accelerate particles to energies exceeding
10^12 electron Volts (eV) and are bright sources of very-high-energy
(VHE) gamma-ray emission, it is not yet known where the VHE emission
originates. Here we report on radio and VHE observations of the radio
galaxy M 87, revealing a period of extremely strong VHE gamma-ray
flares accompanied by a strong increase of the radio flux from its
nucleus. These results imply that charged particles are accelerated to
very high energies in the immediate vicinity of the black hole.
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