from cybhpt_full import _TeukolskyMode as _TeukolskyModeCython
[docs]
class TeukolskyMode:
"""A class for computing Teukolsky modes sourced by a point-particle orbiting in a Kerr background.
Parameters
----------
s : int
The spin weight of the Teukolsky mode.
j : int
The spheroidal harmonic mode number.
m : int
The azimuthal harmonic mode number.
k : int
The polar harmonic mode number.
n : int
The radial harmonic mode number.
geo : KerrGeodesic class instance
KerrGeodesic object containing the background motion of the point-particle source.
auto_solve : bool, optional
If True, the Teukolsky equation is automatically solved upon initialization. Default is False
Attributes
----------
spinweight : int
The spin weight of the Teukolsky mode.
spheroidalmode : int
The spheroidal harmonic mode number.
azimuthalmode : int
The azimuthal harmonic mode number.
radialmode : int
The radial harmonic mode number.
polarmode : int
The polar harmonic mode number.
blackholespin : float
The spin of the black hole in the Kerr background.
frequency : float
The frequency of the Teukolsky mode.
horizonfrequency : float
The frequency of the mode at the horizon.
eigenvalue : float
The spheroidal eigenvalue of the Teukolsky mode.
mincouplingmode : int
The minimum l-mode used for coupling the spherical and spheroidal harmonics
maxcouplingmode : int
The maximum l-mode used for coupling the spherical and spheroidal harmonics
j : int
Alias for spheroidalmode.
m : int
Alias for azimuthalmode.
k : int
Alias for polarmode.
n : int
Alias for radialmode.
omega : float
Alias for frequency.
a : float
Alias for blackholespin.
Methods
-------
solve(geo, method = "AUTO", nsamples = 256, teuk = None, swsh = None)
Solve the Teukolsky equation for the given mode and geodesic.
flipspinweight()
Flip the spin weight of the Teukolsky mode.
flipspinweightandfrequency()
Flip the spin weight and frequency of the Teukolsky mode.
couplingcoefficient(l)
Compute the coupling coefficient for the given l-mode.
radialpoint(pos)
Compute the radial point for the given position.
radialsolution(bc, pos)
Compute the radial solution for the given boundary condition and position.
radialderivative(bc, pos)
Compute the radial derivative for the given boundary condition and position.
radialderivative2(bc, pos)
Compute the second radial derivative for the given boundary condition and position.
homogeneousradialsolution(bc, pos)
Compute the homogeneous radial solution for the given boundary condition and position.
homogeneousradialderivative(bc, pos)
Compute the homogeneous radial derivative for the given boundary condition and position.
homogeneousradialderivative2(bc, pos)
Compute the second homogeneous radial derivative for the given boundary condition and position.
polarpoint(pos)
Compute the polar point for the given position.
polarsolution(pos)
Compute the polar solution for the given position.
polarderivative(pos)
Compute the polar derivative for the given position.
polarderivative2(pos)
Compute the second polar derivative for the given position.
amplitude(bc)
Compute the Teukolsky amplitude for the given boundary condition.
precision(bc)
Compute the precision of the Teukolsky amplitude for the given boundary condition.
"""
def __init__(self, s, j, m, k, n, geo, auto_solve = False):
self.base = _TeukolskyModeCython(s, j, m, k, n, geo.base)
if auto_solve:
self.solve(geo)
@property
def spinweight(self):
return self.base.spinweight
@property
def spheroidalmode(self):
return self.base.spheroidalmode
@property
def azimuthalmode(self):
return self.base.azimuthalmode
@property
def radialmode(self):
return self.base.radialmode
@property
def polarmode(self):
return self.base.polarmode
@property
def blackholespin(self):
return self.base.blackholespin
@property
def frequency(self):
return self.base.frequency
@property
def horizonfrequency(self):
return self.base.horizonfrequency
@property
def eigenvalue(self):
return self.base.eigenvalue
@property
def mincouplingmode(self):
return self.base.mincouplingmode
@property
def maxcouplingmode(self):
return self.base.maxcouplingmode
# some useful aliases
@property
def j(self):
return self.spheroidalmode
@property
def m(self):
return self.azimuthalmode
@property
def k(self):
return self.polarmode
@property
def n(self):
return self.radialmode
@property
def omega(self):
return self.frequency
@property
def a(self):
return self.blackholespin
@property
def couplingcoefficients(self):
return self.base.couplingcoefficients
@property
def polarpoints(self):
return self.base.polarpoints
@property
def polarsolutions(self):
return self.base.polarsolutions
@property
def polarderivatives(self):
return self.base.polarderivatives
@property
def polarderivatives2(self):
return self.base.polarderivatives2
@property
def radialpoints(self):
return self.base.radialpoints
@property
def radialsolutions(self):
return self.base.radialsolutions
@property
def radialderivatives(self):
return self.base.radialderivatives
@property
def radialderivatives2(self):
return self.base.radialderivatives2
@property
def homogeneousradialsolutions(self):
return self.base.homogeneousradialsolutions
@property
def homogeneousradialderivatives(self):
return self.base.homogeneousradialderivatives
@property
def homogeneousradialderivatives2(self):
return self.base.homogeneousradialderivatives2
@property
def amplitudes(self):
return self.base.teukolsky_amplitudes
@property
def precisions(self):
return self.base.teukolsky_amplitude_precisions
[docs]
def solve(self, geo, method = "AUTO", nsamples = 256, teuk = None, swsh = None):
"""Solve the Teukolsky equation for the given mode and geodesic.
Parameters
----------
geo : KerrGeodesic class instance
KerrGeodesic object containing the background motion of the point-particle source.
method : str, optional
The method to use for solving the Teukolsky equation. Default is "AUTO".
nsamples : int, optional
The number of samples to use for the solution. Default is 256.
teuk : RadialTeukolsky, optional
RadialTeukolsky object to use for constructing the radial Green function. Default is None.
swsh : SpheroidalHarmonicMode, optional
SpheroidalHarmonic object to use for coupling with spheroidal harmonics. Default is None.
"""
if teuk is None or swsh is None:
self.base.solve(geo.base, method, nsamples)
else:
self.base.solve(geo.base, method, nsamples, teuk.base, swsh.base)
"""
Flips the spin-weight of the Teukolsky solutions from :math:`s \rightarrow -s`
"""
[docs]
def flipspinweight(self):
self.base.flip_spinweight()
"""
Flips the spin-weight and frequency of the Teukolsky solutions from :math:`s \rightarrow -s` and :math:`\omega \rightarrow -\omega`
"""
[docs]
def flipspinweightandfrequency(self):
"""
Flips the spin-weight and frequency of the Teukolsky solutions from :math:`s \rightarrow -s` and :math:`\omega \rightarrow -\omega`
"""
self.base.flip_spinweight_frequency()
[docs]
def couplingcoefficient(self, l):
"""
Spherical-spheroidal mixing coefficient between a spherical harmonic $l$ mode with a spheroidal $j$ mode.
Parameters
----------
l : int
Spherical harmonic mode.
Returns
-------
float
The coupling coefficient between the spherical harmonic mode `l` and the spheroidal harmonic mode `j`.
"""
return self.base.couplingcoefficient(l)
[docs]
def radialpoint(self, pos):
"""
The radial point for the given position `pos`.
Parameters
----------
pos : int
The radial position.
Returns
-------
float
The radial point at the given position `pos`.
"""
return self.base.radialpoint(pos)
[docs]
def radialsolution(self, bc, pos):
"""
The extended homogeneous radial solution for the given boundary condition `bc` and position `pos`.
Parameters
----------
bc : str
The boundary condition, either "In" for ingoing or "Up" for upgoing.
pos : int
The radial position.
Returns
-------
complex
The radial solution at the given boundary condition `bc` and position `pos`.
"""
return self.base.radialsolution(bc, pos)
[docs]
def radialderivative(self, bc, pos):
"""
The derivative of the extended homogeneous radial solution for the given boundary condition `bc` and position `pos`.
Parameters
----------
bc : str
The boundary condition, either "In" for ingoing or "Up" for upgoing.
pos : int
The radial position.
Returns
-------
complex
The radial derivative at the given boundary condition `bc` and position `pos`.
"""
return self.base.radialderivative(bc, pos)
[docs]
def radialderivative2(self, bc, pos):
"""
The second derivative of the extended homogeneous radial solution for the given boundary condition `bc` and position `pos`.
Parameters
----------
bc : str
The boundary condition, either "In" for ingoing or "Up" for upgoing.
pos : int
The radial position.
Returns
-------
complex
The radial second derivative at the given boundary condition `bc` and position `pos`.
"""
return self.base.radialderivative2(bc, pos)
[docs]
def homogeneousradialsolution(self, bc, pos):
"""
The homogeneous radial solution for the given boundary condition `bc` and position `pos`.
Parameters
----------
bc : str
The boundary condition, either "In" for ingoing or "Up" for upgoing.
pos : int
The radial position.
Returns
-------
complex
The radial solution at the given boundary condition `bc` and position `pos`.
"""
return self.base.homogeneousradialsolution(bc, pos)
[docs]
def homogeneousradialderivative(self, bc, pos):
"""
The radial derivative of the homogeneous radial solution for the given boundary condition `bc` and position `pos`.
Parameters
----------
bc : str
The boundary condition, either "In" for ingoing or "Up" for upgoing.
pos : int
The radial position.
Returns
-------
complex
The radial derivative at the given boundary condition `bc` and position `pos`.
"""
return self.base.homogeneousradialderivative(bc, pos)
[docs]
def homogeneousradialderivative2(self, bc, pos):
"""
The second radial derivative of the homogeneous radial solution for the given boundary condition `bc` and position `pos`.
Parameters
----------
bc : str
The boundary condition, either "In" for ingoing or "Up" for upgoing.
pos : int
The radial position.
Returns
-------
complex
The radial second derivative at the given boundary condition `bc` and position `pos`.
"""
return self.base.homogeneousradialderivative2(bc, pos)
[docs]
def polarpoint(self, pos):
"""
The polar point for the given position `pos`.
Parameters
----------
pos : int
The polar position.
Returns
-------
float
The polar point at the given position `pos`.
"""
return self.base.polarpoint(pos)
[docs]
def polarsolution(self, pos):
"""
The polar solution for the given position `pos`.
Parameters
----------
pos : int
The polar position.
Returns
-------
float
The polar solution at the given position `pos`.
"""
return self.base.polarsolution(pos)
[docs]
def polarderivative(self, pos):
"""
The derivative of the polar solution for the given position `pos`.
Parameters
----------
pos : int
The polar position.
Returns
-------
float
The polar derivative at the given position `pos`.
"""
return self.base.polarderivative(pos)
[docs]
def polarderivative2(self, pos):
"""
The second derivative of the polar solution for the given position `pos`.
Parameters
----------
pos : int
The polar position.
Returns
-------
float
The polar second derivative at the given position `pos`.
"""
return self.base.polarderivative2(pos)
[docs]
def amplitude(self, bc):
"""
The Teukolsky amplitude for the given boundary condition `bc`.
Parameters
----------
bc : str
The boundary condition, either "In" for ingoing or "Up" for upgoing.
Returns
-------
complex
The Teukolsky amplitude at the given boundary condition `bc`.
"""
return self.base.teukolsky_amplitude(bc)
[docs]
def precision(self, bc):
"""
The precision of the Teukolsky amplitude for the given boundary condition `bc`.
Parameters
----------
bc : str
The boundary condition, either "In" for ingoing or "Up" for upgoing.
Returns
-------
float
The precision of the Teukolsky amplitude at the given boundary condition `bc`.
"""
return self.base.teukolsky_amplitude_precision(bc)