Black Hole Shadow as a Test of General Relativity: Quadratic Gravity

Observations of the black hole shadow of supermassive black holes, such as Sagittarius A* at the center of our Milky Way galaxy, allow us to study the properties of black holes and the nature of strong-field gravity. According to the Kerr hypothesis, isolated, stationary, and axisymmetric astrophysical black holes are described by the Kerr metric. The Kerr hypothesis holds in General Relativity and in some modified gravity theories, but there are others in which it is violated. In principle, black hole shadow observations can be used to determine if the Kerr metric is the correct description for black holes, and in turn, they could be used to place constraints on modified gravity theories that do not admit the Kerr solution. We here investigate whether black hole shadow observations can constrain deviations from general relativity, focusing on two well-motivated modified quadratic gravity theories: Einstein-dilaton-Gauss-Bonnet gravity and dynamical Chern-Simons gravity. We show that current constraints on Einstein-dilaton-Gauss-Bonnet gravity are stronger than any that could be placed with black hole shadow observations of supermassive black holes. We also show that the same holds for dynamical Chern-Simons gravity through a systematic bias and a likelihood analysis when considering slowly-rotating supermassive black holes. However, observations of more rapidly-rotating black holes, with dimensionless spins $|\vec{J}|/M^{2}\simeq0.5$, could be used to better constrain dynamical Chern-Simons gravity.