Test of the Einstein Equivalence Principle near the Galactic Center Supermassive Black Hole

During its orbit around the four million solar mass black hole Sagittarius A* the star S2 experiences significant changes in gravitational potential. We use this change of potential to test one part of the Einstein equivalence principle: the local position invariance (LPI). We study the dependency of different atomic transitions on the gravitational potential to give an upper limit on violations of the LPI. This is done by separately measuring the redshift from hydrogen and helium absorption lines in the stellar spectrum during its closest approach to the black hole. For this measurement we use radial velocity data from 2015 to 2018 and combine it with the gravitational potential at the position of S2, which is calculated from the precisely known orbit of S2 around the black hole. This results in a limit on a violation of the LPI of $|{\beta }_{\mathrm{He}}-{\beta }_{\mathrm{H}}|=(2.4\pm 5.1)\times {10}^{-2}$. The variation in potential that we probe with this measurement is six magnitudes larger than possible for measurements on Earth, and a factor of 10 larger than in experiments using white dwarfs. We are therefore testing the LPI in a regime where it has not been tested before.

Figure 1

High signal-to-noise spectrum of the star S2 in the astronomical $K$ band. The spectrum has been produced by combining data from 12 years of observations (adapted from Ref. [28]).

Figure 2

Difference in frequency change for the helium and the hydrogen line as red dots. The dimensionless gravitational potential is shown as a dashed black line. The solid black line shows $\mathrm{\Delta }\beta \mathrm{\Delta }\mathrm{\Phi }/c^2$, where $\mathrm{\Delta }\beta$ is fitted to the data. The gray area shows the 3 sigma values from the fit.

Figure 3

Comparison of selected tests of the LPI with gravitational redshift. Plotted is the variation in potential, which is tested against the measured limit on a violation. The different symbols mark the Pound-Rebka-Snider experiments [47, 48], tests from solar spectral lines [49, 50, 51], tests on rockets and spacecrafts [52, 53, 54], and null redshift experiments [33, 35, 55, 56, 57]