Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole

The 2017 Event Horizon Telescope (EHT) observations of the central source in M87 have led to the first measurement of the size of a black-hole shadow. This observation offers a new and clean gravitational test of the black-hole metric in the strong-field regime. We show analytically that spacetimes that deviate from the Kerr metric but satisfy weak-field tests can lead to large deviations in the predicted black-hole shadows that are inconsistent with even the current EHT measurements. We use numerical calculations of regular, parametric, non-Kerr metrics to identify the common characteristic among these different parametrizations that control the predicted shadow size. We show that the shadow-size measurements place significant constraints on deviation parameters that control the second post-Newtonian and higher orders of each metric and are, therefore, inaccessible to weak-field tests. The new constraints are complementary to those imposed by observations of gravitational waves from stellar-mass sources.

Figure 1

Bound on the deviation parameters (left) ${\alpha }_{13}$ of the JP metric and (right) ${\gamma }_{1,2}$ for the MGBK metric, as a function of spin ($J/M^2$) and for different values of the other metric parameters, placed by the 2017 EHT observations of M87. The shaded areas show the excluded regions of the parameter space. The dashed line shows the analytic result obtained for zero spin. The EHT measurements place constraints predominantly on ${\alpha }_{13}$ (for JP) and ${\gamma }_{1,2}$ (for MGBK), which control the 2 PN expansion of the corresponding metrics (see Table 1).