# Test of Einstein equivalence principle near the Galactic center supermassive black hole

## TL;DR

This study tests the Einstein equivalence principle's local position invariance near the supermassive black hole Sagittarius A* by analyzing atomic spectral lines in star S2's spectrum during its orbit, providing new constraints in a previously untested gravitational regime.

## Contribution

It introduces a novel test of the Einstein equivalence principle's local position invariance in the strong gravitational field near a supermassive black hole using stellar spectral data.

## Key findings

- Set an upper limit on LPI violation of |β_{He}-β_{H}| = (2.4 ± 5.1) × 10^{-2}.
- Probed gravitational potential variation six magnitudes larger than Earth-based tests.
- Extended the testing regime of the LPI to a stronger gravitational environment.

## Abstract

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 $|\beta_{He}-\beta_{H}| = (2.4 \pm 5.1) \cdot 10^{-2}$. The variation in potential that we probe with this measurement is six magnitudes larger than possible for measurements on Earth, and a factor ten larger than in experiments using white dwarfs. We are therefore testing the LPI in a regime where it has not been tested before.