On the presence of a fifth force at the Galactic Center: an update with GRAVITY data and future prospects

In this talk I will present the recent results obtained by the GRAVITY Collaboration on the presence of a Yukawa-like correction to Newtonian gravity at the Galactic Center (GC). The precision of the GRAVITY instrument allowed us to derive the most stringent upper limit for the intensity of the Yukawa contribution (~ α e- λ r) at the GC to be |α| < 0.003 for a scale length λ = 3 x 1013 m  (~ 200 AU), improving by roughly one order of magnitude all estimates obtained in the past. I will also show how the inclusion of multiple stars in the fit can help break the degeneracy between both the parameter α, the black hole mass MBH and the PPN parameters γ and β in the large λ limit, when considering specific alternative theories of gravity.