black_hole_math¶

Math routines for Luminet [1].

This module contains the mathematical routines to calculate the trajectory of photons around a Swarzschild black hole, as described in Luminet [1].

Functions¶

`calc_q`(→ float)	Convert periastron \(P\) to \(Q\)
`calc_b_from_periastron`(→ float)	Get impact parameter \(b\) from the photon periastron \(P\)
`calc_k`(→ float)	Calculate the modulus of the elliptic integral
`calc_k_squared`(p, bh_mass)	Calculate the squared modulus of elliptic integral
`calc_zeta_inf`(→ float)	Calculate \(\zeta_\infty\)
`calc_zeta_r`(→ float)	Calculate \(\zeta_r\)
`calc_cos_gamma`(→ float)	Calculate \(\cos(\gamma)\)
`calc_sn`(→ float)	Calculate the elliptic function \(\text{sn}\)
`calc_radius`(→ float)	Calculate the radius on the black hole accretion disk from a photon's periastron value.
`periastron_optimization_function`(→ float)	Cost function for the optimization of the periastron value.
`solve_for_periastron`(→ float)	Calculate the periastron of a photon trajectory, when the black hole coordinates are known.
`solve_for_impact_parameter`(→ float)	Calculate observer coordinates of a BH frame photon.
`ellipse`(→ float)	Equation of an ellipse
`calc_Z1`(bh_mass, a)	Calculate \(Z1\) for Kerr black holes.
`calc_Z2`(bh_mass, a)	Calculate \(Z2\) for Kerr black holes.
`calc_innermost_stable_orbit`(bh_mass, a)	Calculcate the innermost stable orbit \(r_{ms}\) for a Kerr black hole.
`calc_x0`(bh_mass, a)	Calculcate \(x_0\) for Kerr black holes.
`calc_f_kerr`(bh_mass, a, r)	Calculate the \(f\)-function from Page and Thorne [2] (Equation 12)
`calc_flux_intrinsic_kerr`(bh_mass, a, r, acc)	Calculate the intrinsic flux of the accretion disk of a Kerr black hole, in function of the accretion rate, specific angular momentum, and radius of emission.
`calc_flux_intrinsic_swarzschild`(bh_mass, r, acc)	Calculate the intrinsic flux of a photon.
`calc_flux_observed`(r, acc, bh_mass, redshift_factor)	Calculate the observed bolometric flux of a photon \(F_o\)
`calc_redshift_factor`(radius, angle, incl, bh_mass, b)	Calculate the gravitational redshift factor (ignoring cosmological redshift):