polar_solutions

kerrgeopy.stable.polar_solutions(a, constants, polar_roots)

Computes the polar solutions \(\theta(q_\theta), t^{(\theta)}(q_\theta), \phi^{(\theta)}(q_\theta)\) from equation 6 of Fujita and Hikida. \(q_\theta\) is defined as \(q_\theta = \Upsilon_\theta \lambda = 2\pi \frac{\lambda}{\Lambda_\theta}\). 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 \((\mathcal{E},\mathcal{L},\mathcal{Q})\)

• polar_roots (tuple(double,double)) – tuple of roots \((z_-,z_+)\)

Returns:

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

Return type:

tuple(function, function, function)