Radiating material close to a compact object probes relativistic orbital motion, gravitational redshift and light propagation. A thin disk's inferred inner edge can be compared with the predicted innermost stable circular orbit, while iron-line transfer and thermal-continuum fitting probe complementary aspects of the same geometry. Agreement tests a combined spacetime-and-disk model. A black-hole spin measurement made after imposing a Kerr metric is not alone an independent verification of that metric tensor; geometry tests must vary gravitational predictions and astrophysical nuisance parameters together.
A geometrically thin, optically thick disk has a radially varying effective temperature. Relativistic transport and an atmosphere model convert its thermal spectrum into an inferred emitting area and inner radius. Black-hole mass, distance, inclination and spectral hardening are important external constraints. Selecting thermal-state observations with moderate luminosity limits contamination and the breakdown of the thin-disk approximation. Relating the fitted inner radius to the innermost stable circular orbit remains a physical modeling assumption.
An irradiated accretion disk can produce iron fluorescence with a known local energy scale. relativistic Doppler effect, gravitational redshift, beaming and light bending redistribute those photons into a broadened asymmetric line. The red wing is sensitive to the deepest emitting radii, while inclination and orbital motion influence the profile. Coronal illumination, ionization, absorption and the continuum model must be controlled before inferring an inner radius or testing a spacetime geometry.
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