Deformed black hole in Sagittarius A

We analyze the post-Newtonian orbit of stars around a deformed Kerr black hole. The deformation we consider is class disformal transformations nontrivial solution in scalar-tensor theory which are labeled via parameter $D$. study different limits parameter, and compare trajectories orbiting hole to case spacetime general relativity, up 2PN order. Our findings show that for generic nonzero $D$, no-hair theorem relativity violated, sense hole's quadrupole $Q$ not determined by its mass $M$ angular momentum $J$ through relation $Q=-J^2/M$. Limiting values $D$ provide examples simple exact noncircular metric solutions, whereas particular limit, where $1+D$ small but finite, obtain leading correction Schwarzschild precession due disformality. In this case, constrained using recent measurement pericenter star S2 GRAVITY Collaboration.