calc_Z1

luminet.black_hole_math.calc_Z1(bh_mass, a)

Calculate \(Z1\) for Kerr black holes.

The variable \(Z1\) is used to calculate the innermost orbit for Kerr black holes.

\[Z_1 \equiv 1 + \sqrt[3]{1-a_*^2}\left[ \sqrt[3]{1+a_*} + \sqrt[3]{1-a_*} \right]\]

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.

See also

Page and Thorne [2] Equation 15l

See also

calc_innermost_orbit() for the calculation of the innermost orbit of Kerr black holes.