Probing the black hole metric: Black hole shadows and binary black-hole inspirals

In general relativity, the spacetimes of black holes have three fundamental properties: (i) they are same, to lowest order in spin, as metrics stellar objects; (ii) independent mass when expressed geometric units; and (iii) described by Kerr metric. this paper, we quantify upper bounds on potential black-hole metric deviations imposed observations shadows binary inspirals explore current experimental limits possible violations last two predictions. We find that both types experiments provide correlated constraints deviation parameters primarily $tt$ components areal coordinates. conclude that, currently, there is no evidence for from across 8 orders magnitude 16 curvature spanned holes. Moreover, because particular masses sample gravitational-wave sources, correlations aligned similar magnitudes terms far-field, post-Newtonian predictions metrics. If a future coalescing with low-mass (e.g., $\ensuremath{\sim}3\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$) discovered, degeneracy between can be broken combining inspiral those shadow measurements.