= Two-face dissipation of a Paczyński-Wiita disk
{title2=$D=-\mathcal G\Omega'/(2\pi R)$}
For a <steady accretion disk with arbitrary rotation law> and a <zero-torque inner boundary condition> at $R=3R_S$, the outward <viscous torque in an accretion disk> is $\mathcal G=\dot M(j-j_{\mathrm{in}})$. The dissipation per unit planar area summed over both disk faces is $D=-\mathcal G\Omega'/(2\pi R)=\nu\Sigma(R\Omega')^2$. Integrating $2\pi R D$ gives $L=\dot M GM/(8R_S)=\dot M c^2/16$ in the <Paczyński-Wiita potential>. The radiative flux from one face is $D/2$, preventing a factor-of-two error in the luminosity.
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