The Current Ability to Test Theories of Gravity with Black Hole Shadows
  Our Galactic Center, Sagittarius A* (Sgr A*), is believed to harbour a
supermassive black hole (BH), as suggested by observations tracking individual
orbiting stars. Upcoming sub-millimetre very-long-baseline-interferometry
(VLBI) images of Sgr A* carried out by the Event-Horizon-Telescope
Collaboration (EHTC) are expected to provide critical evidence for the
existence of this supermassive BH. We assess our present ability to use EHTC
images to determine if they correspond to a Kerr BH as predicted by Einstein's
theory of general relativity (GR) or to a BH in alternative theories of
gravity. To this end, we perform general-relativistic magnetohydrodynamical
(GRMHD) simulations and use general-relativistic radiative transfer (GRRT)
calculations to generate synthetic shadow images of a magnetised accretion flow
onto a Kerr BH. In addition, and for the first time, we perform GRMHD
simulations and GRRT calculations for a dilaton BH, which we take as a
representative solution of an alternative theory of gravity. Adopting the VLBI
configuration from the 2017 EHTC campaign, we find that it could be extremely
difficult to distinguish between BHs from different theories of gravity, thus
highlighting that great caution is needed when interpreting BH images as tests
of GR.
