The centre of our Milky Way harbours the closest candidate for a supermassive black hole. The source is thought to be powered by radiatively inefficient accretion of gas from its environment. This form of accretion is a standard mode of energy supply for most galactic nuclei. X-ray measurements have already resolved a tenuous hot gas component from which it can be fed. However, the magnetization of the gas, a crucial parameter determining the structure of the accretion flow, remains unknown. Strong magnetic fields can influence the dynamics of the accretion, remove angular momentum from the infalling gas, expel matter through relativistic jets and lead to the observed synchrotron emission. Here we report multi-frequency measurements with several radio telescopes of a newly discovered pulsar close to the Galactic Centre and show that its unusually large Faraday rotation indicates a dynamically relevant magnetic field near the black hole. If this field is accreted down to the event horizon it provides enough magnetic flux to explain the observed emission from the black hole, from radio to X-rays.
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