Flux module

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Flux module#

API#

The time-averaged rate of change of the orbital energy \(\langle \dot{E}\rangle\), angular momentum \(\langle \dot{L}_z\rangle\), and Carter constant \(\langle \dot{Q}\rangle\) can be expressed in terms of the Teukolsky amplitudes \(Z^\mathrm{Up/In}_{sjmkn}\),

\[\begin{split} \begin{align} \langle \dot{\mathcal{J}} \rangle & = \langle \dot{\mathcal{J}} \rangle^\mathrm{inf} + \langle \dot{\mathcal{J}} \rangle^\mathrm{hor}, \\ &= \sum_{jmkn} \langle \dot{\mathcal{J}} \rangle^\mathrm{inf/hor}_{jmkn}, \\ &= \sum_{jmkn} \alpha_{sjmkn}^{(\mathcal{J})\mathrm{inf/hor}}\left| Z^\mathrm{Up/In}_{sjmkn} \right|^2, \end{align}\end{split}\]
where \(\mathcal{J} = (E, L_z, Q)\), \(\alpha_{sjmkn}^{(\mathcal{J})\mathrm{inf}/\mathrm{hor}}\) are known coefficients, and \(s=0, \pm 2\) produce either scalar or gravitational fluxes, respectively.

The FluxMode class takes as input an instances of the Kerr geodesic class and the Teukolsky class for a mode \((s,j,m,k,n)\), and produces the flux contribution for that given mode.

Docstring for pybhpt.flux

Module containing classes and functions for computing fluxes of energy, angular momentum, and Carter constant in Kerr spacetime.

class pybhpt.flux.FluxList(fluxes=None)[source]

Bases: object

A class for storing fluxes of energy, angular momentum, and Carter constant.

Parameters:

fluxes (list of dicts, optional) – A list containing three dictionaries, each with keys “I” and “H” representing the fluxes at infinity and on the horizon, respectively. If not provided, initializes with zero fluxes for all three components.

Variables:

fluxes (list of dicts) – A list containing three dictionaries, each with keys “I” and “H” representing the fluxes at infinity and on the horizon, respectively. The first dictionary corresponds to energy flux, the second to angular momentum flux, and the third to Carter constant flux.

__call__():

Returns the list of fluxes.

property energy
property angularmomentum
property carterconstant
__call__()[source]

Call self as a function.

class pybhpt.flux.FluxMode(geo, teuk)[source]

Bases: object

A class for computing fluxes of energy, angular momentum, and Carter constant for a given Teukolsky mode.

Parameters:

  • geo (KerrGeodesic class instance) – KerrGeodesic object containing the background motion of the point-particle source.

  • teuk (TeukolskyMode object) – TeukolskyMode object containing mode solutions to the point-particle-sourced Teukolsky equation.

Variables:

  • energy (dict) – A dictionary containing the energy flux at infinity and on the horizon. The keys are “I” for infinity and “H” for the horizon.

  • angularmomentum (dict) – A dictionary containing the angular momentum flux at infinity and on the horizon. The keys are “I” for infinity and “H” for the horizon.

  • carterconstant (dict) – A dictionary containing the Carter constant flux at infinity and on the horizon. The keys are “I” for infinity and “H” for the horizon.

  • fluxes (FluxList) – A FluxList object containing the energy, angular momentum, and Carter constant fluxes.

  • horizonfluxes (list) – A list containing the energy, angular momentum, and Carter constant fluxes on the horizon.

  • infinityfluxes (list) – A list containing the energy, angular momentum, and Carter constant fluxes at infinity.

  • totalfluxes (list) – A list containing the total fluxes, which are the sum of the horizon and infinity fluxes.

property energy
property angularmomentum
property carterconstant
property Edot
property Ldot
property Qdot
property fluxes
property horizonfluxes
property infinityfluxes
property totalfluxes
pybhpt.flux.transform_ELQ_fluxes_to_pex(a, p, e, x, Edot, Lzdot, Qdot)[source]

Transform fluxes of energy, angular momentum, and Carter constant to fluxes of semi-latus rectum, eccentricity, and inclination.

Parameters:

  • a (float or np.ndarray) – Spin parameter of the Kerr black hole.

  • p (float or np.ndarray) – Semi-latus rectum of the orbit.

  • e (float or np.ndarray) – Eccentricity of the orbit.

  • x (float or np.ndarray) – Cosine of the inclination angle of the orbit.

  • Edot (float or np.ndarray) – Flux of energy.

  • Lzdot (float or np.ndarray) – Flux of angular momentum.

  • Qdot (float or np.ndarray) – Flux of Carter constant.

Returns:

A tuple (pdot, edot, xdot) where: - pdot: Flux of semi-latus rectum. - edot: Flux of eccentricity. - xdot: Flux of inclination.

Return type:

tuple of (float or np.ndarray, float or np.ndarray, float or np.ndarray)

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