Metric reconstruction module

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Metric reconstruction module#

API#

pybhpt.metric.gauge_check(gauge)[source]
pybhpt.metric.metric_coefficients_S4dagger_ab(ai, bi, nt, nr, nz, nph, a, r, z)[source]

Compute the metric coefficients for the reconstructed perturbation associated with the S4dagger reconstruction operator.

Parameters:

  • ai (int) – The indices of the tetrad-projected components of the metric perturbation.

  • bi (int) – The indices of the tetrad-projected components of the metric perturbation.

  • nt (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nr (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nz (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nph (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • a (float) – The black hole spin parameter.

  • r (float) – The radial coordinate.

  • z (float) – The polar coordinate (cosine of the polar angle).

Returns:

The computed metric coefficient.

Return type:

float

pybhpt.metric.metric_coefficients_S0dagger_ab(ai, bi, nt, nr, nz, nph, a, r, z)[source]

Compute the metric coefficients for the reconstructed perturbation associated with the S0dagger reconstruction operator.

Parameters:

  • ai (int) – The indices of the tetrad-projected components of the metric perturbation.

  • bi (int) – The indices of the tetrad-projected components of the metric perturbation.

  • nt (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nr (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nz (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nph (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • a (float) – The black hole spin parameter.

  • r (float) – The radial coordinate.

  • z (float) – The polar coordinate (cosine of the polar angle).

Returns:

The computed metric coefficient.

Return type:

float

pybhpt.metric.metric_coefficients_S0dagger(a, b, c, d, q, rvals, zvals)[source]

Compute the metric coefficients for the reconstructed perturbation associated with the S0dagger reconstruction operator.

Parameters:

  • a (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • b (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • c (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • d (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • q (float) – The black hole spin parameter.

  • rvals (numpy.ndarray) – The radial coordinate.

  • zvals (np.ndarray) – The polar coordinate (cosine of the polar angle).

Returns:

A 3D array containing the computed metric coefficients for the S0dagger operator.

Return type:

numpy.ndarray

pybhpt.metric.metric_coefficients_S4dagger(a, b, c, d, q, rvals, zvals)[source]

Compute the metric coefficients for the reconstructed perturbation associated with the S4dagger reconstruction operator.

Parameters:

  • a (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • b (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • c (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • d (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • q (float) – The black hole spin parameter.

  • rvals (numpy.ndarray) – The radial coordinate.

  • zvals (np.ndarray) – The polar coordinate (cosine of the polar angle).

Returns:

A 3D array containing the computed metric coefficients for the S0dagger operator.

Return type:

numpy.ndarray

pybhpt.metric.metric_coefficients(gauge, a, b, c, d, q, rvals, zvals)[source]

Compute the metric coefficients for the reconstructed perturbation associated with the specified gauge.

Parameters:

  • gauge (str) – The gauge to use for the reconstruction. Must be one of the available gauges.

  • a (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • b (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • c (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • d (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • q (float) – The black hole spin parameter.

  • rvals (numpy.ndarray) – The radial coordinate.

  • zvals (np.ndarray) – The polar coordinate (cosine of the polar angle).

Returns:

A 3D array containing the computed metric coefficients for the specified gauge.

Return type:

numpy.ndarray

class pybhpt.metric.MetricCoefficients(gauge, q, r, th)[source]

Bases: object

A class for computing the metric coefficients of the reconstructed perturbation associated with the S0dagger or S4dagger reconstruction operator based on the specified gauge.

Parameters:

  • gauge (str) – The gauge to use for the reconstruction. Must be one of the available gauges.

  • q (float) – The black hole spin parameter.

  • r (numpy.ndarray) – The radial coordinate values.

  • th (numpy.ndarray) – The polar coordinate values (cosine of the polar angle).

Variables:

  • gauge (str) – The gauge used for the reconstruction.

  • blackholespin (float) – The black hole spin parameter.

  • radialpoints (numpy.ndarray) – The radial coordinate values.

  • polarpoints (numpy.ndarray) – The polar coordinate values (cosine of the polar angle).

  • storedcomponents (dict) – A dictionary mapping pairs of indices (a, b) to the index of the stored component in the coefficients array.

  • conjugatecomponents (dict) – A dictionary mapping pairs of indices (a, b) to the index of the conjugate component in the coefficients array.

  • coeffs (numpy.ndarray) – A 7D array containing the computed metric coefficients for the specified gauge.

  • zeros (numpy.ndarray) – A 2D array of zeros with the same shape as the radial and polar coordinate arrays.

hab(a, b, nt, nr, ns, nphi):

Returns the metric coefficient for the specified indices (a, b) and derivative orders (nt, nr, ns, nphi). If the indices are not found in the stored or conjugate components, it returns a zero array.

__call__(a, b, nt, nr, ns, nphi):

Calls the hab method to retrieve the metric coefficient for the specified indices and derivative orders.

hab(a, b, nt, nr, ns, nphi)[source]

Returns the metric coefficient for the specified indices (a, b) and derivative orders (nt, nr, ns, nphi). If the indices are not found in the stored or conjugate components, it returns a zero array.

Parameters:

  • a (int) – The indices of the tetrad-projected components of the metric perturbation.

  • b (int) – The indices of the tetrad-projected components of the metric perturbation.

  • nt (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nr (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • ns (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nphi (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

Returns:

The computed metric coefficient for the specified indices and derivative orders.

Return type:

numpy.ndarray

__call__(a, b, nt, nr, ns, nphi)[source]

Calls the hab method to retrieve the metric coefficient for the specified indices and derivative orders.

Parameters:

  • a (int) – The indices of the tetrad-projected components of the metric perturbation.

  • b (int) – The indices of the tetrad-projected components of the metric perturbation.

  • nt (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nr (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • ns (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

  • nphi (int) – The indices associated with the time, radial, spin, and azimuthal derivative operators.

Returns:

The computed metric coefficient for the specified indices and derivative orders.

Return type:

numpy.ndarray

pybhpt.metric.tetrad_project_l(a, r, z, mu)[source]
pybhpt.metric.tetrad_project_n(a, r, z, mu)[source]
pybhpt.metric.tetrad_project_m(a, r, z, mu)[source]
pybhpt.metric.kinnersley_tetrad_covector(b, q, r, z, mu)[source]
pybhpt.metric.hmunu_BL(gauge, mu, nu, q, r, hab)[source]
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