The M87* Shadow Diameter Against Its Independent Mass: A Ten-Per-Cent Geometric Test

Using the stellar-dynamical mass and the distance adopted by the Event Horizon Telescope collaboration as inputs independent of the ring image itself, the Schwarzschild shadow diameter predicted for M87* is 39.7 microarcseconds, against a measured shadow diameter of 42 plus or minus 3 microarcseconds. The ratio of measured to predicted diameter is 1.058, the absolute difference is 2.3 microarcseconds, and once the 11.8 per cent prediction uncertainty is combined with the measurement uncertainty the difference stands at 0.42 standard deviations. The gravitational radius subtends 3.82 microarcseconds. The test therefore passes at the ten-per-cent level and no further: the budget is dominated by the mass, not by the image. Any alternative geometry whose shadow differs from the Schwarzschild value by less than about ten per cent is unconstrained by this comparison, and any claim of a deviation smaller than that, in either direction, exceeds what the inputs support. All figures are computed from published values under stated assumptions; the study is simulated, not measured.