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Einsteins General Theory of Relativity (GR) successfully describes gravity. The most fundamental predictions of GR are black holes (BHs), but in spite of many convincing BH candidates in the Universe, there is no conclusive experimental proof of their existence using astronomical observations in the electromagnetic spectrum. Are BHs real astrophysical objects? Does GR hold in its most extreme limit or are alternatives needed? The prime target to address these fundamental questions is in the center of our own Galaxy, which hosts the closest and best-constrained supermassive BH candidate in the Universe, Sagittarius A* (Sgr A*). Three different types of experiments hold the promise to test GR in a strong-field regime using observations of Sgr A* with new-generation instruments. The first experiment aims to image the relativistic plasma emission which surrounds the event horizon and forms a shadow cast against the background, whose predicted size (~50 microarcseconds) can now be resolved by upcoming VLBI experiments at mm-waves such as the Event Horizon Telescope (EHT). The second experiment aims to monitor stars orbiting Sgr A* with the upcoming near-infrared interferometer GRAVITY at the Very Large Telescope (VLT). The third experiment aims to time a radio pulsar in tight orbit about Sgr A* using radio telescopes (including the Atacama Large Millimeter Array or ALMA). The BlackHoleCam project exploits the synergy between these three different techniques and aims to measure the main BH parameters with sufficient precision to provide fundamental tests of GR and probe the spacetime around a BH in any metric theory of gravity. Here, we review our current knowledge of the physical properties of Sgr A* as well as the current status of such experimental efforts towards imaging the event horizon, measuring stellar orbits, and timing pulsars around Sgr A*.
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S-stars in the Galactic Center are excellent testbeds of various general relativistic effects. While previous works focus on modeling their orbital motion around Sgr A*--the supermassive black hole in the Galactic Center--here we explore the possibility of using the rotation of S-stars to test the de Sitter precession predicted by general relativity. We show that by reorienting the rotation axes of S-stars, de Sitter precession will change the apparent width of the absorption lines in the stellar spectra. Our numerical simulations suggest that the newly discovered S4714 and S62 are best suited for such a test because of their small pericenter distances relative to Sgr A*. Depending on the initial inclination of the star, the line width would vary by as much as $20-76,{rm km,s^{-1}}$ within a period of $20-40$ years. Such a variation is comparable to the current detection limit. Since the precession rate is sensitive to the orbital eccentricity and stellar quadrupole structure, monitoring the rotation of S-stars could also help us better constrain the orbital elements of the S-stars and their internal structures.
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