Einstein ’ s General Theory of Relativity ( GR ) successfully describes gravity .
Although GR has been accurately tested in weak gravitational fields , it remains largely untested in the general strong field cases .
One of the most fundamental predictions of GR is the existence of black holes ( BH ) .
After the recent direct detection of gravitational waves by LIGO , there is now near conclusive evidence for the existence of stellar-mass BHs .
In spite of this exciting discovery , there is not yet direct evidence of the existence of BHs using astronomical observations in the electromagnetic spectrum .
Are BHs observable 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 Milky Way , 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 consists of making a standard astronomical image of the synchrotron emission from the relativistic plasma accreting onto Sgr A* .
This emission forms a “ shadow ” around the event horizon cast against the background , whose predicted size ( \sim 50 \mu as ) can now be resolved by upcoming very long baseline radio interferometry experiments at mm-waves such as the Event Horizon Telescope ( EHT ) .
The second experiment aims to monitor stars orbiting Sgr A* with the next-generation near-infrared interferometer GRAVITY at the Very Large Telescope ( VLT ) .
The third experiment aims to detect and study 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 contributes directly to them at different levels .
These efforts will eventually enable us to measure fundamental BH parameters ( mass , spin , and quadrupole moment ) with sufficiently high precision to provide fundamental tests of GR ( e.g. , testing the no-hair theorem ) 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* .
We conclude that the Galactic center provides a unique fundamental-physics laboratory for experimental tests of BH accretion and theories of gravity in their most extreme limits .