radial_solutions

kerrgeopy.stable.radial_solutions(a, constants, radial_roots)

Computes the radial solutions \(r(q_r), t^{(r)}(q_r), \phi^{(r)}(q_r)\) from equation 6 of Fujita and Hikida. \(q_r\) is defined as \(q_r = \Upsilon_r \lambda = 2\pi \frac{\lambda}{\Lambda_r}\). Assumes the initial conditions \(r(0) = r_{\text{min}}\) and \(\theta(0) = \theta_{\text{min}}\).

Parameters:

• a (double) – dimensionless spin parameter

• constants (tuple(double,double,double)) – tuple of constants \((\mathcal{E},\mathcal{L},\mathcal{Q})\)

• radial_roots (tuple(double,double,double,double)) – tuple of roots \((r_1,r_2,r_3,r_4)\). Assumes that motion is between \(r_1\) and \(r_2\) and that roots are otherwise in decreasing order.

Returns:

tuple of functions \((r, t^{(r)}, \phi^{(r)})\)

Return type:

tuple(function, function, function)