event horizon — oblate (Kerr)
photon sphere n=0,1,2
accretion disk — Novikov-Thorne
relativistic jet (a=0.998)
ergosphere / frame dragging

spin parameter a = 0.998 M

ISCO r ≈ 1.237 Rs

ergosphere r_erg = 2M (equator)

jet power ∝ a² / (1+√(1−a²))²

frame drag Ω_H = a / 2Mr_+

drag → orbit

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Kerr Metric
ds² = Kerr(r,θ)
Boyer-Lindquist coords। Σ=r²+a²cos²θ, Δ=r²-2Mr+a²। r_+=M+√(M²-a²)। a=0.998 near-extremal।
Ray Tracing
null geodesics
Carter constants। b=L/E impact param। RK4 integration। Photon rings n=0,1,2।
Novikov-Thorne
T ∝ f(r)^(1/4)
F∝(r-r_ISCO)/r⁴। ISCO inner edge। Doppler+grav redshift। T→spectrum map।
Blandford-Znajek
P_jet ∝ a²B²M²
Spin-powered jet। B-field threads horizon। Γ~10। M87*, Cyg A observed।
Ergosphere
r_erg = M+√(M²-a²cos²θ)
Frame dragging zone। Co-rotation mandatory। Penrose process। Oblate spin shape।
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