The Last Clock

Light paths numerically integrate the null-geodesic Hamiltonian in horizon-penetrating Kerr–Schild coordinates. Disk brightness includes relativistic frequency shifting; color and the plunging-region heat contours are an inward velocity/temperature approximation. Visible light only uses exposure-normalized thermal-spectrum samples; the contour overlay remains available in either spectrum mode. It does not predict absolute luminosity. Indirect images are classified by accumulated ray bending and coverage-reduced as their photon subrings become unresolved. The grid, probe marker, and horizon interior are explanatory views. Mass changes physical size, orbital time, and tidal gradient; the rendered geometry stays normalized in rₛ so those scales can be compared directly. Horizon diameter is area-equivalent; tidal Δa is the Schwarzschild comparison across two meters at rₛ. A bounded off-axis lens shift keeps the Kerr shadow framed without rotating the observer; the clock probe follows the equatorial local frame.