Constraints on alternative theories of gravity with observations of the Galactic Center

TL;DR

This paper reviews observational techniques used to test alternative gravity theories at the Galactic Center, emphasizing the importance of relativistic corrections in stellar orbit analysis and shadow measurements.

Contribution

It discusses the current observational methods and highlights the necessity of incorporating relativistic effects for accurate interpretation of data in testing gravity theories.

Findings

Relativistic corrections are essential for precise stellar orbit analysis.

First post-Newtonian correction is necessary for gravitational redshift in S2 star.

VLBI observations require strong gravity approximations for small structure analysis.

Abstract

To evaluate a potential usually one analyzes trajectories of test particles. For the Galactic Center case astronomers use bright stars or photons, so there are two basic observational techniques to investigate a gravitational potential, namely, (a) monitoring the orbits of bright stars near the Galactic Center as it is going on with 10m Keck twin and four 8m VLT telescopes equipped with adaptive optics facilities (in addition, recently the IR interferometer GRAVITY started to operate with VLT); (b) measuring the size and shape of shadows around black hole with VLBI-technique using telescopes operating in mm-band. At the moment, one can use a small relativistic correction approach for stellar orbit analysis, however, in the future the approximation will not be precise enough due to enormous progress of observational facilities and recently the GRAVITY team found that the first post-Newtonian correction has to be taken into account for the gravitational redshift in the S2 star orbit case. Meanwhile for smallest structure analysis in VLBI observations one really needs a strong gravitational field approximation. We discuss results of observations and their interpretations.