waveformtools.extrapolate
Methods for waveform extrapolation.
Functions
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Convert the isotropic co-ordinate radius parameter r in the ETK simulations |
Extract a numerical waveform to null infinity using perturbative techniques. This is : |
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Extract a numerical waveform to null infinity using perturbative techniques. This is : |
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Extract a numerical waveform to null infinity using perturbative techniques. This is : |
- waveformtools.extrapolate.r_to_ra_conversion(coord_radius, mass=1, spin=0)[source]
- Convert the isotropic co-ordinate radius parameter r in the ETK simulations
into the approximate areal radius.
- Parameters:
- coord_radius: float
The coordinate radius in the Einstein toolkit
- mass: float, optional
The sum of the quasi-local horizon (Christodolou) masses of the black holes. Defaults to 1.
- spin: float, optional
The magnitude of the spin of the system, as approximated by a single Kerr black hole far away from the system. Defaults to 0.
- Returns:
- areal_radius: float
The appriximate areal radius of the sphere.
Notes
Assumes that the system interoir to the sphere at co-ordinate radius r_coord is well approximated by a Kerr black hole.
References
Nakano et al., (2015), Phys. Rev. D 91, 104022, in-text below Eq.[30].
- waveformtools.extrapolate.waveextract_to_inf_perturbative_one_order(u_ret, rPsi4_rlm, areal_radius=500, ell=2)[source]
- Extract a numerical waveform to null infinity using perturbative techniques. This is :
accurate to second order in \(1/r\).
accurate to first order in Kerr mass and spin.
corrects for spheroidal harmonics
- Parameters:
- u_ret: 1d array
The retarted time array at the location r = areal_radius.
- rPsi4_rlm: 1d array
The extracted Weyl scalar \(r\Psi_{4\ell m}\) data array
- areal_radius: 1d array
The areal radius of the extraction sphere.
- mass: float
The total horizon mass of the system.
- ell: int
The polar quantum number \(\ell\).
- emm: int
The azimuthal quantum number \(m\).
- Returns:
- rPsi4_inflm: 1d array
The waveform extracted to null infninity \(\mathcal{I}^+\)
References
This implements the definition in Nakano et al., (2015), Phys. Rev. D 91, 104022 Eq.[29].
- waveformtools.extrapolate.waveextract_to_inf_perturbative_two_order(rPsi4_rlm, delta_t, areal_radius=500, mass=1, ell=2)[source]
- Extract a numerical waveform to null infinity using perturbative techniques. This is :
accurate to second order in \(1/r\).
accurate to first order in Kerr mass and spin.
corrects for spheroidal harmonics
- Parameters:
- rPsi4_rlm: 1d array
The extracted Weyl scalar \(r\Psi_{4\ell m}\) data array.
- delta_t: float
The time stepping.
- areal_radius: 1d array
The areal radius of the extraction sphere.
- mass: float
The total horizon mass of the system.
- spin: float, optional
The effective spin of the spacetime. Defaults to 0.
- ell: int
The polar quantum number \(\ell\).
- emm: int
The azimuthal quantum number \(m\).
- Returns:
- rPsi4_inflm: 1d array
The waveform extracted to null infninity \(\mathcal{I}^+\)
References
This implements the definition in Nakano et al., (2015), Phys. Rev. D 91, 104022 Eq.[29].
- waveformtools.extrapolate.waveextract_to_inf_perturbative_twop5_order(rPsi4_rlm, delta_t, areal_radius=500, mass=1, spin=0, ell=2, emm=2)[source]
- Extract a numerical waveform to null infinity using perturbative techniques. This is :
accurate to second order in \(1/r\).
accurate to first order in Kerr mass and spin.
corrects for spheroidal harmonics
- Parameters:
- rPsi4_rlm: 1d array
The extracted Weyl scalar \(r\Psi_{4\ell m}\) data array
- delta_t: float
The time stepping.
- areal_radius: 1d array
The areal radius of the extraction sphere.
- mass: float
The total horizon mass of the system.
- spin: float, optional
The effective spin of the spacetime. Defaults to 0.
- ell: int
The polar quantum number \(\ell\).
- emm: int
The azimuthal quantum number \(m\).
- Returns:
- rPsi4_inflm: 1d array
The waveform extracted to null infninity \(\mathcal{I}^+\)
References
This implements the definition in Nakano et al., (2015), Phys. Rev. D 91, 104022 Eq.[29].