Shadow Centroid Shift as a Spin and Inclination Observable: A Leading-Order Budget

A rotating black hole's shadow is not centred on the hole's mass centre: frame dragging displaces the bright, approaching side and shifts the shadow's centroid by an amount that grows with spin and with the sine of the inclination. Under the leading-order model stated here, displacement = 2 a sin(i) theta_g, the shift for M87* at the jet-inferred inclination of 17 degrees and spin 0.9 is only 2.01 microarcseconds, while an edge-on hole at spin 0.99 would show 7.56 microarcseconds, 18.0 per cent of the shadow diameter. For Sagittarius A* the corresponding figures are 7.99 microarcseconds at 60 degrees and 10.15 edge-on at high spin. The M87* shift is therefore below any realistic astrometric reach, a negative result for that source, while a favourably inclined Sagittarius A* offers a shift at the edge of plausibility for future arrays with an external astrometric reference. Computed under a stated leading-order model; simulated, not measured.