The team compared the position and velocity measurements from GRAVITY and SINFONI respectively, along with previous observations of S2 using other instruments, with the predictions of Newtonian gravity, general relativity and other theories of gravity. The new results are inconsistent with Newtonian predictions and in excellent agreement with the predictions of general relativity.
The new measurements clearly reveal an effect called gravitational redshift. Light from the star is stretched to longer wavelengths by the very strong gravitational field of the black hole. And the change in the wavelength of light from S2 agrees precisely with that predicted by Einstein’s theory of general relativity. This is the first time that this deviation from the predictions of the simpler Newtonian theory of gravity has been observed in the motion of a star around a supermassive black hole.
A copy of the paper (or maybe a preprint) can be found here.
It bears repeating: the more they test it, the more convincing it becomes!