Units: radii in gravitational radii rg = GM/c². Gas orbits at the Kerr circular-orbit frequency Ω = c³ / (GM (r3/2 + a*)) and spirals inward only outside the innermost stable circular orbit (ISCO), given by the Bardeen-Press-Teukolsky formula risco = 3 + Z₂ ∓ √((3−Z₁)(3+Z₁+2Z₂)).
Radiative efficiency is the binding energy lost down to the ISCO: η = 1 − Eisco, with E = (1 − 2/r + a*/r3/2) / √(1 − 3/r + 2a*/r3/2) (prograde). It is 5.7% for a* = 0 and about 32% for a* = 0.998. Accretion rate: Ṁ = L / (η c²).
Temperature follows the Shakura-Sunyaev thin-disk law (Newtonian form with the inner edge at the ISCO): σT⁴ = 3GMṀ / (8π r³) · (1 − √(rin/r)). The spectrum is a sum of blackbodies, Lν = Σ 2·πBν(T)·2πr dr (multicolour disk).
Doppler beaming: gas with line-of-sight speed β has its brightness scaled by δ³, δ = 1/(γ(1 − β cosθ)), so the approaching side looks brighter at high inclination. Eddington limit: LEdd = 4πGMmpc/σT ≈ 1.26×10³¹ W (M/M☉).
Simplifications: Newtonian temperature profile (no full Novikov-Thorne relativistic corrections), no ray tracing or gravitational lensing, no corona, no disk winds; speeds shown are Keplerian estimates. The view shows geometry, not a rendered image of a real object. Educational physics only.