calc_innermost_stable_orbit¶

luminet.black_hole_math.calc_innermost_stable_orbit(bh_mass, a)¶

Calculcate the innermost stable orbit \(r_{ms}\) for a Kerr black hole.

A larger specific angular momentum \(a\) will yield innermost orbits closer to the black hole.

\[\begin{split}\begin{align*} r_{ms} &= Mx_0^2 \\ x_0^2 &= 3 + Z_2 - sgn(a_*)\sqrt{(3-Z_1)(3+Z_1+2Z_2) } \end{align*}\end{split}\]

Parameters:

bh_mass (float) – Mass of the black hole.
a (float) – Specific angular momentum of the black hole. Should always be between \(-1\) and \(1\). \(a > 0\) if the accretion disk orbits in the same direction as the hole rotates; \(a < 0\) if it orbits in the opposite direction.