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Searching for space-time variations of the constants of Nature is a promisingway to search for new physics beyond General Relativity and the standard modelmotivated by unification theories and models of dark matter and dark energy. Wepropose a new way to search for a variation of the fine-structure constantusing measurements of late-type evolved giant stars from the S-star clusterorbiting the supermassive black hole in our Galactic Center. A measurement ofthe difference between distinct absorption lines (with different sensitivity tothe fine structure constant) from a star leads to a direct estimate of avariation of the fine structure constant between the star's location and Earth.Using spectroscopic measurements of 5 stars, we obtain a constraint on therelative variation of the fine structure constant below $10^{-5}$. This is thefirst time a varying constant of Nature is searched for around a black hole andin a high gravitational potential. This analysis shows new ways the monitoringof stars in the Galactic Center can be used to probe fundamental physics.

Search for a Variation of the Fine Structure around the Supermassive Black Hole in Our Galactic Center