Hertz point-particle mode module

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Hertz point-particle mode module#

API#

pybhpt.hertz.hertz_IRG(Zin, Zup, j, m, k, a, omega, lambdaCH)[source]

Convert Teukolsky amplitudes to Hertz potential in the IRG gauge.

pybhpt.hertz.hertz_ORG(Zin, Zup, j, m, k, a, omega, lambdaCH)[source]

Convert Teukolsky amplitudes to Hertz potential in the ORG gauge.

pybhpt.hertz.hertz_SRG(Zin, Zup, j, m, k, a, omega, lambdaCH)[source]

Convert Teukolsky amplitudes to Hertz potential in the SRG gauge.

pybhpt.hertz.hertz_ARG(Zin, Zup, j, m, k, a, omega, lambdaCH)[source]

Convert Teukolsky amplitudes to Hertz potential in the ARG gauge.

pybhpt.hertz.teuk_to_hertz_amplitude(gauge, Zin, Zup, j, m, k, a, omega, lambdaCH)[source]
pybhpt.hertz.test_hertz_mode(j, m, k, n, geo)[source]
pybhpt.hertz.gauge_check(gauge)[source]

Check if the provided gauge is supported. Raises a TypeError if the gauge is not supported.

class pybhpt.hertz.HertzMode(teuk, gauge)[source]

Bases: object

Class that produces a Hertz potential mode given a Teukolsky object and a gauge. This class is a wrapper around the Cython implementation of the Hertz potential and provides a Python interface to the underlying C++ code.

Parameters:

  • teuk (Teukolsky) – The Teukolsky object to be used for the Hertz potential.

  • gauge (str) – The gauge to be used for the Hertz potential. Must be one of the following: - “IRG” - “ORG” - “SRG0” - “SRG4” - “ARG0” - “ARG4”

Variables:

  • base (HertzModeCython) – The underlying Cython implementation of the Hertz potential mode.

  • gauge (str) – The gauge used for the Hertz potential.

  • sampleR (int) – The number of radial samples used in the Hertz potential mode solutions

  • sampleTh (int) – The number of polar samples used in the Hertz potential mode solutions

  • spinweight (int) – The spin weight of the Hertz potential mode.

  • spheroidalmode (int) – The spheroidal mode number of the Hertz potential mode.

  • azimuthalmode (int) – The azimuthal mode number of the Hertz potential mode.

  • radialmode (int) – The radial mode number of the Hertz potential mode.

  • polarmode (int) – The polar mode number of the Hertz potential mode.

  • blackholespin (float) – The spin of the black hole associated with the background spacetime.

  • frequency (float) – The frequency of the Hertz potential mode.

  • horizonfrequency (float) – The frequency of the Hertz potential mode at the horizon.

  • eigenvalue (complex) – The spheroidal eigenvalue associated with the Hertz potential 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

  • minscalarcouplingmode (int) – The minimum l-mode used for coupling the scalar harmonics

  • maxscalarcouplingmode (int) – The maximum l-mode used for coupling the scalar 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.

  • Properties

  • ----------

  • couplingcoefficients (np.ndarray) – The coupling coefficients for the Hertz potential mode.

  • scalarcouplingcoefficients (np.ndarray) – The scalar coupling coefficients for the Hertz potential mode.

  • polarpoints (np.ndarray) – The polar points used in the Hertz potential mode solutions.

  • polarsolutions (np.ndarray) – The polar mode solutions of the Hertz potential.

  • polarderivatives (np.ndarray) – Derivatives of the polar mode solutions of the Hertz potential.

  • polarderivatives2 (np.ndarray) – Second derivatives of the polar mode solutions of the Hertz potential.

  • radialpoints (np.ndarray) – The radial points used in the Hertz potential mode solutions.

  • radialsolutions (np.ndarray) – The radial mode solutions of the Hertz potential.

  • radialderivatives (np.ndarray) – Derivatives of the radial mode solutions of the Hertz potential.

  • radialderivatives2 (np.ndarray) – Second derivatives of the radial mode solutions of the Hertz potential.

solve()[source]

Solve the Hertz potential mode equations.

couplingcoefficient(l)[source]

Returns the coupling coefficient for the given l-mode.

scalarcouplingcoefficient(l)[source]

Returns the scalar coupling coefficient for the given l-mode.

radialpoint(pos)[source]

Returns the radial point corresponding to the given position.

radialsolution(bc, pos)[source]

Returns the radial solution for the given boundary condition and position.

radialderivative(bc, pos)[source]

Returns the radial derivative for the given boundary condition and position.

radialderivative2(bc, pos)[source]

Returns the second radial derivative for the given boundary condition and position.

homogeneousradialsolution(bc, pos)[source]

Returns the homogeneous radial solution for the given boundary condition and position.

homogeneousradialderivative(bc, pos)[source]

Returns the homogeneous radial derivative for the given boundary condition and position.

homogeneousradialderivative2(bc, pos)[source]

Returns the second homogeneous radial derivative for the given boundary condition and position.

polarpoint(pos)[source]

Returns the polar point corresponding to the given position.

polarsolution(pos)[source]

Returns the polar solution for the given position.

polarderivative(pos)[source]

Returns the polar derivative for the given position.

polarderivative2(pos)[source]

Returns the second polar derivative for the given position.

amplitude(bc)[source]

Returns the Hertz amplitude for the given boundary condition.

__call__(r, deriv=0)[source]

Returns the radial Hertz potential mode evaluated at the given radial values r. Alternatively, it can return the radial derivative if deriv is set to 1 or 2. The radial values r must lie outside the source region defined by the radial points. If r contains values inside the source region, a ValueError is raised.

property spinweight
property spheroidalmode
property azimuthalmode
property radialmode
property polarmode
property blackholespin
property frequency
property horizonfrequency
property eigenvalue
property mincouplingmode
property maxcouplingmode
property minscalarcouplingmode
property maxscalarcouplingmode
property j
property m
property k
property n
property omega
property a
property couplingcoefficients
property scalarcouplingcoefficients
property polarpoints
property polarsolutions
property polarderivatives
property polarderivatives2
property radialpoints
property radialsolutions
property radialderivatives
property radialderivatives2
property amplitudes
solve()[source]
couplingcoefficient(l)[source]
scalarcouplingcoefficient(l)[source]
radialpoint(pos)[source]
radialsolution(bc, pos)[source]
radialderivative(bc, pos)[source]
radialderivative2(bc, pos)[source]
homogeneousradialsolution(bc, pos)[source]
homogeneousradialderivative(bc, pos)[source]
homogeneousradialderivative2(bc, pos)[source]
polarpoint(pos)[source]
polarsolution(pos)[source]
polarderivative(pos)[source]
polarderivative2(pos)[source]
amplitude(bc)[source]
__call__(r, deriv=0)[source]

Evaluate the radial Hertz potential mode at the given radial values r. If deriv is set to 0, it returns the Hertz potential mode. If deriv is set to 1, it returns the first radial derivative. If deriv is set to 2, it returns the second radial derivative.

Parameters:

  • r (array-like) – The radial values at which to evaluate the Hertz potential mode.

  • deriv (int, optional) – The order of the radial derivative to compute. Default is 0 (no derivative).

Returns:

The evaluated Hertz potential mode or its radial derivative at the given radial values r.

Return type:

numpy.ndarray

Raises:

ValueError – If any of the radial values r lie within the source region defined by the radialpoints.

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