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Update code to use BMSTransformation class and add function to map ABD object to the frame of another #85

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Nov 8, 2023
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3 changes: 3 additions & 0 deletions scri/asymptotic_bondi_data/__init__.py
Original file line number Diff line number Diff line change
Expand Up @@ -180,6 +180,7 @@ def interpolate(self, new_times):
# interpolate frame data if necessary
if self.frame.shape[0] == self.n_times:
import quaternion

new_abd.frame = quaternion.squad(self.frame, self.t, new_times)
return new_abd

Expand All @@ -203,10 +204,12 @@ def interpolate(self, new_times):
bondi_rest_mass,
bondi_four_momentum,
bondi_angular_momentum,
CWWY_angular_momentum,
bondi_dimensionless_spin,
bondi_boost_charge,
bondi_CoM_charge,
supermomentum,
)

from .map_to_superrest_frame import map_to_superrest_frame
from .map_to_abd_frame import map_to_abd_frame
45 changes: 41 additions & 4 deletions scri/asymptotic_bondi_data/bms_charges.py
Original file line number Diff line number Diff line change
Expand Up @@ -5,8 +5,10 @@
### class. In particular, they assume that the first argument, `self` is an instance of
### AsymptoticBondData. They should probably not be used outside of that class.

import scri
import numpy as np
from math import sqrt, pi
import spherical_functions as sf


def mass_aspect(self, truncate_ell=max):
Expand Down Expand Up @@ -83,7 +85,7 @@ def bondi_four_momentum(self):
return charge_vector_from_aspect(charge_aspect)


def bondi_angular_momentum(self, output_dimensionless=False):
def bondi_angular_momentum(self):
"""Compute the total Bondi angular momentum vector

i (ψ₁ + σ ðσ̄)
Expand All @@ -99,6 +101,37 @@ def bondi_angular_momentum(self, output_dimensionless=False):
return charge_vector_from_aspect(charge_aspect)[:, 1:]


def CWWY_angular_momentum(self):
"""Compute the Chen/Wang/Wang/Yau angular momentum vector.

See Eq. (5) of https://arxiv.org/abs/2102.03235

"""
ell_max = 1 # Compute only the parts we need, ell<=1
supertranslation_potential_data = scri.asymptotic_bondi_data.map_to_superrest_frame.𝔇inverse(
np.array(self.sigma.ethbar_GHP.ethbar_GHP + self.sigma.bar.eth_GHP.eth_GHP), self.ell_max
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Is it faster to just compute self.sigma.ethbar_GHP.ethbar_GHP and take twice the real part?

)
supertranslation_potential = scri.ModesTimeSeries(
sf.SWSH_modes.Modes(
supertranslation_potential_data,
spin_weight=0,
ell_min=0,
ell_max=self.ell_max,
multiplication_truncator=max,
),
time=self.t,
)
charge_aspect = (
1j
* (
self.psi1.truncate_ell(ell_max)
+ self.sigma.multiply(self.sigma.bar.eth_GHP, truncator=lambda tup: ell_max)
+ supertranslation_potential.multiply(self.mass_aspect().eth_GHP, truncator=lambda tup: ell_max)
)
).view(np.ndarray)
return charge_vector_from_aspect(charge_aspect)[:, 1:]


def bondi_dimensionless_spin(self):
"""Compute the dimensionless Bondi spin vector"""
N = self.bondi_boost_charge()
Expand All @@ -112,7 +145,7 @@ def bondi_dimensionless_spin(self):
vhat = v.copy()
t_idx = v_norm != 0 # Get the indices for timesteps with non-zero velocity
vhat[t_idx] = v[t_idx] / v_norm[t_idx, np.newaxis]
gamma = (1 / np.sqrt(1 - v_norm ** 2))[:, np.newaxis]
gamma = (1 / np.sqrt(1 - v_norm**2))[:, np.newaxis]
J_dot_vhat = np.einsum("ij,ij->i", J, vhat)[:, np.newaxis]
spin_charge = (gamma * (J + np.cross(v, N)) - (gamma - 1) * J_dot_vhat * vhat) / M_sqr
return spin_charge
Expand Down Expand Up @@ -209,15 +242,19 @@ def supermomentum(self, supermomentum_def, **kwargs):
if supermomentum_def.lower() in ["bondi-sachs", "bs"]:
supermomentum = self.psi2 + self.sigma.grid_multiply(self.sigma.bar.dot, **kwargs)
elif supermomentum_def.lower() in ["moreschi", "m"]:
supermomentum = self.psi2 + self.sigma.grid_multiply(self.sigma.bar.dot, **kwargs) + self.sigma.bar.eth_GHP.eth_GHP
supermomentum = (
self.psi2 + self.sigma.grid_multiply(self.sigma.bar.dot, **kwargs) + self.sigma.bar.eth_GHP.eth_GHP
)
elif supermomentum_def.lower() in ["geroch", "g"]:
supermomentum = (
self.psi2
+ self.sigma.grid_multiply(self.sigma.bar.dot, **kwargs)
+ 0.5 * (self.sigma.bar.eth_GHP.eth_GHP - self.sigma.ethbar_GHP.ethbar_GHP)
)
elif supermomentum_def.lower() in ["geroch-winicour", "gw"]:
supermomentum = self.psi2 + self.sigma.grid_multiply(self.sigma.bar.dot, **kwargs) - self.sigma.ethbar_GHP.ethbar_GHP
supermomentum = (
self.psi2 + self.sigma.grid_multiply(self.sigma.bar.dot, **kwargs) - self.sigma.ethbar_GHP.ethbar_GHP
)
else:
raise ValueError(
f"Supermomentum defintion '{supermomentum_def}' not recognized. Please choose one of "
Expand Down
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