{c}

Let $r_S=2GM/c^2$. In the <Paczyński-Wiita potential>, <circular orbit> balance and the <radial epicyclic frequency> formula give
$$
\Omega^2=\frac{GM}{r(r-r_S)^2},\quad
h=\frac{\sqrt{GM}\,r^{3/2}}{r-r_S},\quad
\kappa_r^2=\frac{GM(r-3r_S)}{r(r-r_S)^3}.
$$
Thus the <innermost stable circular orbit> lies at $r=3r_S$. Its <specific orbital energy> is $-c^2/16$, giving a zero-torque <radiative efficiency of black-hole accretion> of $1/16$. The model reproduces the Schwarzschild inner orbit exactly but approximates its relativistic energy and frequency. https://arxiv.org/abs/0904.0913[Abramowicz's derivation] explains the potential's relation to the Schwarzschild effective potential.


 Paczyński-Wiita circular orbit

ID: paczynski-wiita-circular-orbit