plunging_orbit_initial_phases#

kerrgeopy.initial_conditions.plunging_orbit_initial_phases(a, initial_position, initial_velocity, constants=None, radial_roots=None, tol=0.0001)[source]#

Computes the initial phases \((q_{t_0},q_{r_0},q_{\theta_0},q_{\phi_0})\) of a plunging orbit with the given initial conditions. Computes phases with respect to the starting point \((t_0,r_0,\theta_0,\phi_0) = (0,r_\text{min},\theta_{\text{min}},0)\).

Parameters:

  • a (double) – spin parameter

  • initial_position (tuple(double,double,double,double)) – initial position \((t_0,r_0,\theta_0,\phi_0)\)

  • initial_velocity (tuple(double,double,double,double)) – initial four-velocity \((u^t_0,u^r_0,u^\theta_0,u^\phi_0)\)

  • constants (tuple(double,double,double), optional) – constants of motion \((\mathcal{E},\mathcal{L},\mathcal{Q})\) can be passed in to avoid recomputing them

  • radial_roots (tuple(double,double,double,double), optional) – radial roots \((r_1,r_2,r_3,r_4)\) can be passed in to avoid recomputing them

  • tol (double, optional) – numerical tolerance used when checking for turning points, defaults to 1e-4

Returns:

tuple of initial phases \((q_{t_0},q_{r_0},q_{\theta_0},q_{\phi_0})\)

Return type:

tuple(double,double,double,double)