Constraining a disformal Schwarzschild black hole in DHOST theories with the orbit of the S2 star

Abstract: With the observed data of the S2 orbit around the black hole Sgr A$^*$ and the Markov Chain Monte Carlo method, we make a constraint on parameters of a disformal Schwarzschild black hole in quadratic degenerate higher-order scalar-tensor (DHOST) theories. This black hole belongs to a class of non-stealth solutions and owns an extra disformal parameter described the deviation from general relativity. Our results show that the best fit value of the disformal parameter is positive. However, in the range of $1\sigma$, we also find that general relativity remains to be consistent with the observation of the S2 orbit.