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The centre of the Milky Way hosts a supermassive black hole of 4 millionsolar masses called Sagittarius A*. This object has been observed for more than20 years in the near infrared. This has confirmed some effects of GeneralRelativity. In addition, recurrent observations have made it possible to detectflares, i.e. a much larger flux than the average, with a variability of theorder of 30 minutes to 1 hour. In 2018, GRAVITY, using the 4 large telescopesof the VLTI/ESO, observed an orbital motion of the source of these flares. Thisthesis focuses on the modelling of these flares, using models of varyingcomplexity, including one based on the phenomenon of magnetic reconnection. Thelatter corresponds to an abrupt change in the magnetic configuration around theblack hole, releasing a large amount of energy. We are also looking at theproblem of polarisation in General Relativity.

Extreme Astrophysics with GRAVITY : energetic outbursts on the edge of the event horizon of the Galaxy's central black hole