waveformtools.extrapolate

Methods for waveform extrapolation.

Functions

r_to_ra_conversion(coord_radius[, mass, spin])

Convert the isotropic co-ordinate radius parameter r in the ETK simulations

waveextract_to_inf_perturbative_one_order(...)

Extract a numerical waveform to null infinity using perturbative techniques. This is :

waveextract_to_inf_perturbative_two_order(...)

Extract a numerical waveform to null infinity using perturbative techniques. This is :

waveextract_to_inf_perturbative_twop5_order(...)

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].