Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <cstddef>
7 :
8 : #include "DataStructures/ComplexDataVector.hpp"
9 : #include "DataStructures/ComplexModalVector.hpp"
10 : #include "DataStructures/DataBox/PrefixHelpers.hpp"
11 : #include "DataStructures/SpinWeighted.hpp"
12 : #include "DataStructures/Tensor/TypeAliases.hpp"
13 : #include "Evolution/Systems/Cce/BoundaryDataTags.hpp"
14 : #include "Evolution/Systems/Cce/Tags.hpp"
15 : #include "Utilities/TMPL.hpp"
16 :
17 : /// \cond
18 : class DataVector;
19 : template <typename TagsList>
20 : class Variables;
21 : namespace gsl {
22 : template <class T>
23 : class not_null;
24 : } // namespace gsl
25 : /// \endcond
26 :
27 : namespace Cce {
28 :
29 : /*!
30 : * \brief Constructs the collocation values for \f$\cos(\phi)\f$,
31 : * \f$\cos(\theta)\f$, \f$\sin(\phi)\f$, and \f$\sin(\theta)\f$, returned by
32 : * `not_null` pointer in that order.
33 : *
34 : * \details These are needed for coordinate transformations from the input
35 : * Cartesian-like coordinates.
36 : */
37 1 : void trigonometric_functions_on_swsh_collocation(
38 : gsl::not_null<Scalar<DataVector>*> cos_phi,
39 : gsl::not_null<Scalar<DataVector>*> cos_theta,
40 : gsl::not_null<Scalar<DataVector>*> sin_phi,
41 : gsl::not_null<Scalar<DataVector>*> sin_theta, size_t l_max);
42 :
43 : /*!
44 : * \brief Creates both the Jacobian and inverse Jacobian between Cartesian and
45 : * spherical coordinates, and the coordinates themselves
46 : *
47 : * \details The `cartesian_to_spherical_jacobian` is
48 : * \f$dx^i/d\tilde{x}^{\tilde j}\f$,
49 : * where the Cartesian components are in order \f$x^i = \{x, y, z\}\f$
50 : * and the spherical coordinates are
51 : * \f$\tilde{x}^{\tilde j} = \{r, \theta, \phi\}\f$.
52 : * The Cartesian coordinates given are the standard unit sphere coordinates:
53 : *
54 : * \f{align*}{
55 : * x &= \cos(\phi) \sin(\theta)\\
56 : * y &= \sin(\phi) \sin(\theta)\\
57 : * z &= \cos(\theta)
58 : * \f}
59 : *
60 : * \note These Jacobians are adjusted to improve regularity near the pole, in
61 : * particular the \f$\partial \phi / \partial x^i\f$ components have been scaled
62 : * by \f$\sin \theta\f$ (omitting a \f$1/\sin(\theta)\f$) and the
63 : * \f$\partial x^i/\partial \phi\f$ components have been scaled by
64 : * \f$1/\sin(\theta)\f$ (omitting a \f$\sin(\theta)\f$). The reason is that in
65 : * most careful calculations, these problematic sin factors can actually be
66 : * omitted because they cancel. In cases where they are actually required, they
67 : * must be put in by hand.
68 : */
69 1 : void cartesian_to_spherical_coordinates_and_jacobians(
70 : gsl::not_null<tnsr::I<DataVector, 3>*> unit_cartesian_coords,
71 : gsl::not_null<SphericaliCartesianJ*> cartesian_to_spherical_jacobian,
72 : gsl::not_null<CartesianiSphericalJ*>
73 : inverse_cartesian_to_spherical_jacobian,
74 : const Scalar<DataVector>& cos_phi, const Scalar<DataVector>& cos_theta,
75 : const Scalar<DataVector>& sin_phi, const Scalar<DataVector>& sin_theta,
76 : double extraction_radius);
77 :
78 : /*
79 : * \brief Compute \f$g_{i j}\f$, \f$g^{i j}\f$, \f$\partial_i g_{j k}\f$, and
80 : * \f$\partial_t g_{i j}\f$ from input libsharp-compatible modal spatial
81 : * metric quantities.
82 : *
83 : * \details This function interpolates the modes of
84 : * input \f$g_{ij}\f$, \f$\partial_r g_{i j}\f$, and \f$\partial_r g_{i j}\f$ to
85 : * the libsharp-compatible grid. This function then applies the necessary
86 : * jacobian factors and angular derivatives to determine the full \f$\partial_i
87 : * g_{j k}\f$.
88 : */
89 0 : void cartesian_spatial_metric_and_derivatives_from_modes(
90 : gsl::not_null<tnsr::ii<DataVector, 3>*> cartesian_spatial_metric,
91 : gsl::not_null<tnsr::II<DataVector, 3>*> inverse_cartesian_spatial_metric,
92 : gsl::not_null<tnsr::ijj<DataVector, 3>*> d_cartesian_spatial_metric,
93 : gsl::not_null<tnsr::ii<DataVector, 3>*> dt_cartesian_spatial_metric,
94 : gsl::not_null<Scalar<SpinWeighted<ComplexModalVector, 0>>*>
95 : interpolation_modal_buffer,
96 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
97 : interpolation_buffer,
98 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> eth_buffer,
99 : const tnsr::ii<ComplexModalVector, 3>& spatial_metric_coefficients,
100 : const tnsr::ii<ComplexModalVector, 3>& dr_spatial_metric_coefficients,
101 : const tnsr::ii<ComplexModalVector, 3>& dt_spatial_metric_coefficients,
102 : const CartesianiSphericalJ& inverse_cartesian_to_spherical_jacobian,
103 : size_t l_max);
104 :
105 : /*!
106 : * \brief Compute \f$\beta^{i}\f$, \f$\partial_i \beta^{j}\f$, and
107 : * \f$\partial_t \beta^i\f$ from input libsharp-compatible modal spatial
108 : * metric quantities.
109 : *
110 : * \details This function interpolates the modes of
111 : * input \f$\beta^i\f$, \f$\partial_r \beta^i\f$, and \f$\partial_r \beta^i\f$
112 : * to the libsharp-compatible grid. This function then applies the necessary
113 : * jacobian factors and angular derivatives to determine the full \f$\partial_i
114 : * \beta^i\f$.
115 : */
116 1 : void cartesian_shift_and_derivatives_from_modes(
117 : gsl::not_null<tnsr::I<DataVector, 3>*> cartesian_shift,
118 : gsl::not_null<tnsr::iJ<DataVector, 3>*> d_cartesian_shift,
119 : gsl::not_null<tnsr::I<DataVector, 3>*> dt_cartesian_shift,
120 : gsl::not_null<Scalar<SpinWeighted<ComplexModalVector, 0>>*>
121 : interpolation_modal_buffer,
122 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
123 : interpolation_buffer,
124 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> eth_buffer,
125 : const tnsr::I<ComplexModalVector, 3>& shift_coefficients,
126 : const tnsr::I<ComplexModalVector, 3>& dr_shift_coefficients,
127 : const tnsr::I<ComplexModalVector, 3>& dt_shift_coefficients,
128 : const CartesianiSphericalJ& inverse_cartesian_to_spherical_jacobian,
129 : size_t l_max);
130 :
131 : /*!
132 : * \brief Compute \f$\alpha\f$, \f$\partial_i \alpha\f$, and
133 : * \f$\partial_t \beta^i\f$ from input libsharp-compatible modal spatial
134 : * metric quantities.
135 : *
136 : * \details This function interpolates the modes of input \f$\alpha\f$,
137 : * \f$\partial_r \alpha\f$, and \f$\partial_r \alpha\f$ to the
138 : * libsharp-compatible grid. This function then applies the necessary jacobian
139 : * factors and angular derivatives to determine the full \f$\partial_i
140 : * \alpha\f$.
141 : */
142 1 : void cartesian_lapse_and_derivatives_from_modes(
143 : gsl::not_null<Scalar<DataVector>*> cartesian_lapse,
144 : gsl::not_null<tnsr::i<DataVector, 3>*> d_cartesian_lapse,
145 : gsl::not_null<Scalar<DataVector>*> dt_cartesian_lapse,
146 : gsl::not_null<Scalar<SpinWeighted<ComplexModalVector, 0>>*>
147 : interpolation_modal_buffer,
148 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
149 : interpolation_buffer,
150 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> eth_buffer,
151 : const Scalar<ComplexModalVector>& lapse_coefficients,
152 : const Scalar<ComplexModalVector>& dr_lapse_coefficients,
153 : const Scalar<ComplexModalVector>& dt_lapse_coefficients,
154 : const CartesianiSphericalJ& inverse_cartesian_to_spherical_jacobian,
155 : size_t l_max);
156 :
157 : /*!
158 : * \brief Computes spatial derivatives of cartesian metric, shift, and lapse
159 : * from nodal metric quantities on a spherical worldtube.
160 : *
161 : * \details See the details for
162 : * `cartesian_spatial_metric_and_derivatives_from_modes`,
163 : * `cartesian_shift_and_derivatives_from_modes`, and
164 : * `cartesian_lapse_and_derivatives_from_modes` ignoring the transformation from
165 : * modal to nodal (since the metric quantities are already in nodal form).
166 : */
167 1 : void deriv_cartesian_metric_lapse_shift_from_nodes(
168 : gsl::not_null<tnsr::ijj<DataVector, 3>*> d_cartesian_spatial_metric,
169 : gsl::not_null<tnsr::iJ<DataVector, 3>*> d_cartesian_shift,
170 : gsl::not_null<tnsr::i<DataVector, 3>*> d_cartesian_lapse,
171 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> buffer,
172 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> eth_buffer,
173 : const tnsr::ii<DataVector, 3>& cartesian_spatial_metric,
174 : const tnsr::ii<DataVector, 3>& dr_cartesian_spatial_metric,
175 : const tnsr::I<DataVector, 3>& cartesian_shift,
176 : const tnsr::I<DataVector, 3>& dr_cartesian_shift,
177 : const Scalar<DataVector>& cartesian_lapse,
178 : const Scalar<DataVector>& dr_cartesian_lapse,
179 : const CartesianiSphericalJ& inverse_cartesian_to_spherical_jacobian,
180 : size_t l_max);
181 :
182 : /*!
183 : * \brief Computes the spacetime metric and its first derivative in the
184 : * intermediate radial null coordinates
185 : *
186 : * \details These components are obtained by the steps in
187 : * Section II-A of \cite Barkett2019uae, which is based on the computation from
188 : * Section 4.3 of \cite Bishop1998uk. The most direct comparison is to be made
189 : * with equation (31) of \cite Barkett2019uae, which gives the null metric
190 : * components explicitly. The time derivative is then (using notation from
191 : * equation (31) of \cite Barkett2019uae):
192 : *
193 : * \f{align}{
194 : * \partial_{\bar u} g_{\bar u \bar \lambda} =
195 : * \partial_{\bar u} g_{\bar \lambda \bar \lambda} =
196 : * \partial_{\bar u} g_{\bar \lambda \bar A} &= 0 \\
197 : * \partial_{\bar u} g_{\bar u \bar u} &=
198 : * \partial_{\breve t} g_{\breve t \breve t} \\
199 : * \partial_{\bar u} g_{\bar u \bar A} &=
200 : * \frac{\partial \breve x^{\breve i}}{\partial \bar x^{\bar A}}\\
201 : * g_{\breve i \breve t}
202 : * \partial_{\bar u} g_{\bar A \bar B}
203 : * &= \frac{\partial \breve x^{\breve i}}{\partial \bar x^{\bar A}}
204 : * \frac{\partial \breve x^{\breve j}}{\partial \bar x^{\bar B}}
205 : * g_{\breve i \breve j}
206 : * \f}
207 : */
208 1 : void null_metric_and_derivative(
209 : gsl::not_null<tnsr::aa<DataVector, 3, Frame::RadialNull>*> du_null_metric,
210 : gsl::not_null<tnsr::aa<DataVector, 3, Frame::RadialNull>*> null_metric,
211 : const SphericaliCartesianJ& cartesian_to_spherical_jacobian,
212 : const tnsr::aa<DataVector, 3>& dt_spacetime_metric,
213 : const tnsr::aa<DataVector, 3>& spacetime_metric);
214 :
215 : /*!
216 : * \brief Computes the spatial unit normal vector \f$s^i\f$ to the spherical
217 : * worldtube surface and its first time derivative.
218 : *
219 : * \details Refer to equation (20) of \cite Barkett2019uae for the expression of
220 : * the spatial unit normal vector, and equation (23) of \cite Barkett2019uae for
221 : * the first time derivative. Refer to \cite Bishop1998uk for more exposition
222 : * about the overall construction of the coordinate transformations used for the
223 : * intermediate null coordinates.
224 : */
225 1 : void worldtube_normal_and_derivatives(
226 : gsl::not_null<tnsr::I<DataVector, 3>*> worldtube_normal,
227 : gsl::not_null<tnsr::I<DataVector, 3>*> dt_worldtube_normal,
228 : const Scalar<DataVector>& cos_phi, const Scalar<DataVector>& cos_theta,
229 : const tnsr::aa<DataVector, 3>& spacetime_metric,
230 : const tnsr::aa<DataVector, 3>& dt_spacetime_metric,
231 : const Scalar<DataVector>& sin_phi, const Scalar<DataVector>& sin_theta,
232 : const tnsr::II<DataVector, 3>& inverse_spatial_metric);
233 :
234 : /*!
235 : * \brief Computes the null 4-vector \f$l^\mu\f$ on the worldtube surface that
236 : * is to be used as the CCE hypersurface generator, and the first time
237 : * derivative \f$\partial_u l^\mu\f$.
238 : *
239 : * \details For mathematical description of our choice of the null generator,
240 : * refer to equation (22) of \cite Barkett2019uae, and for the first time
241 : * derivative see (25) of \cite Barkett2019uae. Refer to \cite Bishop1998uk for
242 : * more exposition about the overall construction of the coordinate
243 : * transformations used for the intermediate null coordinates.
244 : */
245 1 : void null_vector_l_and_derivatives(
246 : gsl::not_null<tnsr::A<DataVector, 3>*> du_null_l,
247 : gsl::not_null<tnsr::A<DataVector, 3>*> null_l,
248 : const tnsr::I<DataVector, 3>& dt_worldtube_normal,
249 : const Scalar<DataVector>& dt_lapse,
250 : const tnsr::aa<DataVector, 3>& dt_spacetime_metric,
251 : const tnsr::I<DataVector, 3>& dt_shift, const Scalar<DataVector>& lapse,
252 : const tnsr::aa<DataVector, 3>& spacetime_metric,
253 : const tnsr::I<DataVector, 3>& shift,
254 : const tnsr::I<DataVector, 3>& worldtube_normal);
255 :
256 : /*!
257 : * \brief Computes the partial derivative of the spacetime metric and inverse
258 : * spacetime metric in the intermediate null radial coordinates with respect to
259 : * the null generator \f$l^\mu\f$
260 : *
261 : * \details For full expressions of the \f$l^\mu \partial_\mu g_{a b}\f$ and
262 : * \f$l^\mu \partial_\mu g^{a b}\f$ computed in this function, see equation (31)
263 : * and (32) of \cite Barkett2019uae. Refer to \cite Bishop1998uk for more
264 : * exposition about the overall construction of the coordinate transformations
265 : * used for the intermediate null coordinates.
266 : */
267 1 : void dlambda_null_metric_and_inverse(
268 : gsl::not_null<tnsr::aa<DataVector, 3, Frame::RadialNull>*>
269 : dlambda_null_metric,
270 : gsl::not_null<tnsr::AA<DataVector, 3, Frame::RadialNull>*>
271 : dlambda_inverse_null_metric,
272 : const AngulariCartesianA& angular_d_null_l,
273 : const SphericaliCartesianJ& cartesian_to_spherical_jacobian,
274 : const tnsr::iaa<DataVector, 3>& phi,
275 : const tnsr::aa<DataVector, 3>& dt_spacetime_metric,
276 : const tnsr::A<DataVector, 3>& du_null_l,
277 : const tnsr::AA<DataVector, 3, Frame::RadialNull>& inverse_null_metric,
278 : const tnsr::A<DataVector, 3>& null_l,
279 : const tnsr::aa<DataVector, 3>& spacetime_metric);
280 :
281 : /*!
282 : * \brief Computes the Bondi radius of the worldtube.
283 : *
284 : * \details Note that unlike the Cauchy coordinate radius, the Bondi radius is
285 : * not constant over the worldtube. Instead, it is obtained by the determinant
286 : * of the angular part of the metric in the intermediate null coordinates (see
287 : * \cite Barkett2019uae).
288 : *
289 : * \f[
290 : * r = \left(\frac{\det g_{A B}}{ q_{A B}}\right)^{1/4},
291 : * \f]
292 : *
293 : * where \f$q_{A B}\f$ is the unit sphere metric.
294 : */
295 1 : void bondi_r(gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> bondi_r,
296 : const tnsr::aa<DataVector, 3, Frame::RadialNull>& null_metric);
297 :
298 : /*!
299 : * \brief Computes the full 4-dimensional partial of the Bondi radius with
300 : * respect to the intermediate null coordinates.
301 : *
302 : * \details The expression evaluated is obtained from differentiating the
303 : * determinant equation for `bondi_r`, from (35) of \cite Barkett2019uae :
304 : *
305 : * \f[
306 : * \partial_\alpha r = \frac{r}{4} \left(g^{A B} \partial_\alpha g_{A B}
307 : * - \frac{\partial_\alpha \det q_{A B}}{\det q_{A B}}\right)
308 : * \f]
309 : *
310 : * Note that for the angular derivatives, we just numerically differentiate
311 : * using the utilities in `Spectral::Swsh::angular_derivative()`. For the time
312 : * and radial derivatives, the second term in the above equation vanishes.
313 : */
314 1 : void d_bondi_r(
315 : gsl::not_null<tnsr::a<DataVector, 3, Frame::RadialNull>*> d_bondi_r,
316 : const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
317 : const tnsr::aa<DataVector, 3, Frame::RadialNull>& dlambda_null_metric,
318 : const tnsr::aa<DataVector, 3, Frame::RadialNull>& du_null_metric,
319 : const tnsr::AA<DataVector, 3, Frame::RadialNull>& inverse_null_metric,
320 : size_t l_max);
321 :
322 : /*!
323 : * \brief Compute the complex angular dyads used to define the spin-weighted
324 : * scalars in the CCE system.
325 : *
326 : * \details We use the typically chosen angular dyads in CCE
327 : * \cite Barkett2019uae \cite Bishop1997ik :
328 : *
329 : * \f{align*}{
330 : * q_A &= \{-1, -i \sin(\theta)\}\\
331 : * q^A &= \left\{-1, -i \frac{1}{\sin \theta}\right\}
332 : * \f}
333 : *
334 : * However, to maintain regularity and for compatibility with the more regular
335 : * Jacobians from `Cce::cartesian_to_spherical_coordinates_and_jacobians()`, in
336 : * the code we omit the factors of \f$\sin \theta\f$ from the above equations.
337 : */
338 1 : void dyads(
339 : gsl::not_null<tnsr::i<ComplexDataVector, 2, Frame::RadialNull>*> down_dyad,
340 : gsl::not_null<tnsr::I<ComplexDataVector, 2, Frame::RadialNull>*> up_dyad);
341 :
342 : /*!
343 : * \brief Compute the \f$\beta\f$ (lapse) function for the CCE Bondi-like
344 : * metric.
345 : *
346 : * \details The Bondi-like metric has \f$g^{u r} = - e^{2 \beta}\f$, and the
347 : * value of \f$\beta\f$ is obtained from the intermediate null metric by (see
348 : * equation (51) of \cite Barkett2019uae) using:
349 : *
350 : * \f[
351 : * \beta = -\frac{1}{2} \ln \partial_{\lambda} r
352 : * \f]
353 : */
354 1 : void beta_worldtube_data(
355 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> beta,
356 : const tnsr::a<DataVector, 3, Frame::RadialNull>& d_bondi_r);
357 :
358 : /*!
359 : * \brief Compute the \f$U\f$ (shift) function for the CCE Bondi-like metric.
360 : *
361 : * \details The Bondi-like metric has \f$g^{r A} = -e^{-2 \beta} U^A\f$, and the
362 : * spin-weighted vector \f$U = U^A q_A\f$. The value of \f$U^A\f$ can be
363 : * computed from the intermediate null metric quantities (see equation (54) of
364 : * \cite Barkett2019uae) using:
365 : *
366 : * \f[
367 : * U = -(\partial_\lambda r g^{\lambda A} + \partial_B r g^{A B}) q_A
368 : * / \partial_\lambda r \f]
369 : *
370 : */
371 1 : void bondi_u_worldtube_data(
372 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> bondi_u,
373 : const tnsr::i<ComplexDataVector, 2, Frame::RadialNull>& dyad,
374 : const tnsr::a<DataVector, 3, Frame::RadialNull>& d_bondi_r,
375 : const tnsr::AA<DataVector, 3, Frame::RadialNull>& inverse_null_metric);
376 :
377 : /*!
378 : * \brief Compute the \f$W\f$ (mass aspect) function for the CCE Bondi-like
379 : * metric.
380 : *
381 : * \details The Bondi-like metric has \f$g^{rr} = e^{-2 \beta}(1 + r W)\f$. The
382 : * value of \f$W\f$ can be computed from the null metric quantities (see
383 : * equation (55) of \cite Barkett2019uae) using:
384 : *
385 : * \f[
386 : * W = \frac{1}{r} \left(-1
387 : * + \frac{g^{\lambda \lambda} (\partial_\lambda r)^2
388 : * + 2 \partial_\lambda r \left(\partial_A r g^{\lambda A}
389 : * - \partial_u r\right) + \partial_A r \partial_B r g^{A B}}
390 : * {\partial_\lambda r}\right) \f]
391 : */
392 1 : void bondi_w_worldtube_data(
393 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> bondi_w,
394 : const tnsr::a<DataVector, 3, Frame::RadialNull>& d_bondi_r,
395 : const tnsr::AA<DataVector, 3, Frame::RadialNull>& inverse_null_metric,
396 : const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r);
397 :
398 : /*!
399 : * \brief Compute the \f$J\f$ (intuitively similar to the transverse-traceless
400 : * part of the angular metric) function for the CCE Bondi-like metric.
401 : *
402 : * \details The Bondi-like metric has \f$J = \frac{1}{2 r^2} q^A q^B g_{A B}\f$.
403 : * This expression holds both for the right-hand side in the Bondi coordinates
404 : * and for the right-hand side in the intermediate null coordinates (see
405 : * equation (45) of \cite Barkett2019uae).
406 : */
407 1 : void bondi_j_worldtube_data(
408 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*> bondi_j,
409 : const tnsr::aa<DataVector, 3, Frame::RadialNull>& null_metric,
410 : const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
411 : const tnsr::I<ComplexDataVector, 2, Frame::RadialNull>& dyad);
412 :
413 : /*!
414 : * \brief Compute the radial derivative of the angular metric spin-weighted
415 : * scalar \f$\partial_r J\f$ in the CCE Bondi-like metric.
416 : *
417 : * \details The radial derivative of the angular spin-weighted scalar \f$J\f$
418 : * can be computed from the null metric components by (c.f. equation (47) of
419 : * \cite Barkett2019uae):
420 : *
421 : * \f[
422 : * \partial_r J = \frac{\partial_\lambda J}{\partial_\lambda r} =
423 : * \frac{q^A q^B \partial_\lambda g_{A B} / (2 r^2)
424 : * - 2 \partial_\lambda r J / r}{\partial_\lambda r}
425 : * \f]
426 : */
427 1 : void dr_bondi_j(
428 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*> dr_bondi_j,
429 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
430 : denominator_buffer,
431 : const tnsr::aa<DataVector, 3, Frame::RadialNull>& dlambda_null_metric,
432 : const tnsr::a<DataVector, 3, Frame::RadialNull>& d_bondi_r,
433 : const Scalar<SpinWeighted<ComplexDataVector, 2>>& bondi_j,
434 : const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
435 : const tnsr::I<ComplexDataVector, 2, Frame::RadialNull>& dyad);
436 :
437 : /*!
438 : * \brief Compute the second derivative of the Bondi radius with respect to the
439 : * intermediate null coordinate radius \f$\partial_\lambda^2 r\f$.
440 : *
441 : * \details To determine this second derivative quantity without resorting to
442 : * depending on second-derivative metric inputs, we need to take advantage of
443 : * one of the Einstein field equations. Combining equations (53) and (52) of
444 : * \cite Barkett2019uae, we have:
445 : *
446 : * \f[
447 : * \partial_\lambda^2 r = \frac{-r}{4} \left(
448 : * \partial_\lambda J \partial_\lambda \bar J - (\partial_\lambda K)^2\right)
449 : * \f],
450 : *
451 : * where the first derivative of \f$K\f$ can be obtained from \f$K = \sqrt{1 + J
452 : * \bar J}\f$ and the first derivative of \f$J\f$ can be obtained from (47) of
453 : * \cite Barkett2019uae
454 : */
455 1 : void d2lambda_bondi_r(
456 : gsl::not_null<Scalar<DataVector>*> d2lambda_bondi_r,
457 : const tnsr::a<DataVector, 3, Frame::RadialNull>& d_bondi_r,
458 : const Scalar<SpinWeighted<ComplexDataVector, 2>>& dr_bondi_j,
459 : const Scalar<SpinWeighted<ComplexDataVector, 2>>& bondi_j,
460 : const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r);
461 :
462 : /*!
463 : * \brief Compute the Bondi metric contribution \f$Q\f$ (radial derivative of
464 : * shift).
465 : *
466 : * \details The definition of \f$Q\f$ in terms of the Bondi metric components is
467 : *
468 : * \f[
469 : * Q = q^A e^{-2 \beta} g_{A B} \partial_r U^B.
470 : * \f]
471 : *
472 : * $Q$ can be derived from the intermediate null metric quantities via (see
473 : * equations (56) and (57) of \cite Barkett2019uae)
474 : *
475 : * \f[
476 : * \partial_\lambda U = - \left(\partial_\lambda g^{\lambda A}
477 : * + \frac{\partial_A \partial_\lambda r}{\partial_\lambda r} g^{A B}
478 : * + \frac{\partial_B r}{\partial_\lambda r} \partial_\lambda g^{A B}\right) q_A
479 : * + 2 \partial_\lambda \beta (U + g^{\lambda A} q_A)
480 : * \f]
481 : *
482 : * and
483 : *
484 : * \f[
485 : * Q = r^2 (J \partial_\lambda \bar U + K \partial_\lambda U)
486 : * \f]
487 : *
488 : * also provided is \f$\partial_r U\f$, which is separately useful to cache for
489 : * other intermediate steps in the CCE computation.
490 : */
491 1 : void bondi_q_worldtube_data(
492 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> bondi_q,
493 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> dr_bondi_u,
494 : const Scalar<DataVector>& d2lambda_r,
495 : const tnsr::AA<DataVector, 3, Frame::RadialNull>&
496 : dlambda_inverse_null_metric,
497 : const tnsr::a<DataVector, 3, Frame::RadialNull>& d_bondi_r,
498 : const tnsr::i<ComplexDataVector, 2, Frame::RadialNull>& dyad,
499 : const tnsr::i<DataVector, 2, Frame::RadialNull>& angular_d_dlambda_r,
500 : const tnsr::AA<DataVector, 3, Frame::RadialNull>& inverse_null_metric,
501 : const Scalar<SpinWeighted<ComplexDataVector, 2>>& bondi_j,
502 : const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
503 : const Scalar<SpinWeighted<ComplexDataVector, 1>>& bondi_u);
504 :
505 : /*!
506 : * \brief Compute the Bondi metric contribution \f$(\partial_u J)_{y} \equiv
507 : * H\f$ (the retarded time derivative evaluated at fixed $y$ coordinate) on the
508 : * worldtube boundary.
509 : *
510 : * \details The numerical time derivative (along the worldtube, rather than
511 : * along the surface of constant Bondi \f$r\f$) is computed by (see equation
512 : * (48) of \cite Barkett2019uae)
513 : *
514 : * \f[
515 : * (\partial_u J)_y = \frac{1}{2 r^2} q^A q^B \partial_u g_{A B}
516 : * - \frac{2 \partial_u r}{r} J
517 : * \f]
518 : *
519 : * \note There is the regrettable notation difference with the primary reference
520 : * for these formulas \cite Barkett2019uae in that we denote with \f$H\f$ the
521 : * time derivative at constant numerical radius, where \cite Barkett2019uae uses
522 : * \f$H\f$ to denote the time derivative at constant Bondi radius.
523 : */
524 1 : void bondi_h_worldtube_data(
525 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*> bondi_h,
526 : const tnsr::a<DataVector, 3, Frame::RadialNull>& d_bondi_r,
527 : const Scalar<SpinWeighted<ComplexDataVector, 2>>& bondi_j,
528 : const tnsr::aa<DataVector, 3, Frame::RadialNull>& du_null_metric,
529 : const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
530 : const tnsr::I<ComplexDataVector, 2, Frame::RadialNull>& dyad);
531 :
532 : /*!
533 : * \brief Compute the Bondi metric contribution \f$(\partial_u J)_r\f$ (the
534 : * retarded time derivative at fixed coordinate $r$) on the worldtube boundary.
535 : *
536 : * \details The numerical time derivative (along the surface of constant r, not
537 : * along the worldtube) is computed by (see equation (50) of
538 : * \cite Barkett2019uae)
539 : *
540 : * \f[
541 : * \partial_u J = \frac{1}{2 r^2} q^A q^B \left(\partial_u g_{A B}
542 : * - \frac{ \partial_u r}{ \partial_\lambda r} \partial_\lambda g_{A B}\right)
543 : * \f]
544 : *
545 : * \note There is the regrettable notation difference with the primary reference
546 : * for these formulas \cite Barkett2019uae in that we denote with \f$H\f$ the
547 : * time derivative at constant numerical radius, where \cite Barkett2019uae uses
548 : * \f$H\f$ to denote the time derivative at constant Bondi radius.
549 : */
550 1 : void du_j_worldtube_data(
551 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*> du_bondi_j,
552 : const tnsr::a<DataVector, 3, Frame::RadialNull>& d_bondi_r,
553 : const Scalar<SpinWeighted<ComplexDataVector, 2>>& bondi_j,
554 : const tnsr::aa<DataVector, 3, Frame::RadialNull>& du_null_metric,
555 : const tnsr::aa<DataVector, 3, Frame::RadialNull>& dlambda_null_metric,
556 : const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
557 : const tnsr::I<ComplexDataVector, 2, Frame::RadialNull>& dyad);
558 :
559 : /*!
560 : * \brief Convert real scalar to complex spinweighted scalar
561 : */
562 1 : void klein_gordon_psi_worldtube_data(
563 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> kg_psi,
564 : const Scalar<DataVector>& csw_psi);
565 :
566 : /*!
567 : * \brief Compute the time derivative of the scalar for cce and store as a
568 : * complex spinweighted scalar
569 : */
570 1 : void klein_gordon_pi_worldtube_data(
571 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> kg_pi,
572 : const Scalar<DataVector>& csw_pi, const tnsr::i<DataVector, 3>& csw_phi,
573 : const Scalar<DataVector>& lapse, const tnsr::I<DataVector, 3>& shift);
574 :
575 : namespace Tags {
576 : /*!
577 : * \brief The collection of tags mutated by `create_bondi_boundary_data` (and
578 : * `create_klein_gordon_boundary_data` if Klein-Gordon variables are included)
579 : *
580 : * \details This list is used in the evolution of `CharacteristicExtract`
581 : */
582 : template <template <typename> class BoundaryPrefix,
583 : bool IncludeKleinGordon = false>
584 1 : using characteristic_worldtube_boundary_tags = db::wrap_tags_in<
585 : BoundaryPrefix,
586 : tmpl::append<
587 : tmpl::list<Tags::BondiBeta, Tags::BondiU, Tags::Dr<Tags::BondiU>,
588 : Tags::BondiQ, Tags::BondiW, Tags::BondiJ,
589 : Tags::Dr<Tags::BondiJ>, Tags::BondiH, Tags::Du<Tags::BondiJ>,
590 : Tags::BondiR, Tags::Du<Tags::BondiR>, Tags::DuRDividedByR>,
591 : tmpl::conditional_t<
592 : IncludeKleinGordon,
593 : tmpl::list<Cce::Tags::KleinGordonPsi, Cce::Tags::KleinGordonPi>,
594 : tmpl::list<>>>>;
595 :
596 : /*!
597 : * \brief The collection of tags for worldtube quantities that need to be
598 : * written to disk during the Cauchy evolution that the `CharacateristicExtract`
599 : * need.
600 : *
601 : * \details This list is used when writing Bondi quantities to disk. For the
602 : * combined ScalarTensor system, this list also includes the Klein-Gordon scalar
603 : * variables.
604 : */
605 : template <template <typename> class BoundaryPrefix = Cce::Tags::BoundaryValue,
606 : bool IncludeKleinGordon = false>
607 1 : using worldtube_boundary_tags_for_writing = db::wrap_tags_in<
608 : BoundaryPrefix,
609 : tmpl::append<
610 : tmpl::list<Cce::Tags::BondiBeta, Cce::Tags::Dr<Cce::Tags::BondiJ>,
611 : Cce::Tags::Du<Cce::Tags::BondiR>, Cce::Tags::BondiJ,
612 : Cce::Tags::Du<Cce::Tags::BondiJ>, Cce::Tags::BondiQ,
613 : Cce::Tags::BondiR, Cce::Tags::BondiU, Cce::Tags::BondiW>,
614 : tmpl::conditional_t<
615 : IncludeKleinGordon,
616 : tmpl::list<Cce::Tags::KleinGordonPsi, Cce::Tags::KleinGordonPi>,
617 : tmpl::list<>>>>;
618 :
619 0 : using klein_gordon_worldtube_boundary_tags =
620 : tmpl::list<Tags::BoundaryValue<Tags::KleinGordonPsi>,
621 : Tags::BoundaryValue<Tags::KleinGordonPi>>;
622 : } // namespace Tags
623 :
624 : /*!
625 : * \brief Process the worldtube data from generalized harmonic quantities
626 : * to desired Bondi quantities, placing the result in the passed
627 : * `Variables`.
628 : *
629 : * \details
630 : * The mathematics are a bit complicated for all of the coordinate
631 : * transformations that are necessary to obtain the Bondi gauge quantities.
632 : * For full mathematical details, see the documentation for functions in
633 : * `BoundaryData.hpp` and \cite Barkett2019uae \cite Bishop1998uk.
634 : *
635 : * This function takes as input the full set of Generalized harmonic metric data
636 : * on a two-dimensional surface of constant \f$r\f$ and \f$t\f$ in numerical
637 : * coordinates.
638 : *
639 : * Sufficient tags to provide full worldtube boundary data at a particular
640 : * time are set in `bondi_boundary_data`. In particular, the set of tags in
641 : * `Tags::characteristic_worldtube_boundary_tags` in the provided `Variables`
642 : * are assigned to the worldtube boundary values associated with the input
643 : * metric components.
644 : *
645 : * The majority of the mathematical transformations are implemented as a set of
646 : * individual cascaded functions below. The details of the manipulations that
647 : * are performed to the input data may be found in the individual functions
648 : * themselves, which are called in the following order:
649 : * - `trigonometric_functions_on_swsh_collocation()`
650 : * - `gr::shift()`
651 : * - `gr::lapse()`
652 : * - `worldtube_normal_and_derivatives()`
653 : * - `gr::spacetime_normal_vector()`
654 : * - `gh::time_deriv_of_lapse()`
655 : * - `gh::time_deriv_of_shift()`
656 : * - `null_vector_l_and_derivatives()`
657 : * - `cartesian_to_spherical_coordinates_and_jacobians()`
658 : * - `null_metric_and_derivative()`
659 : * - `dlambda_null_metric_and_inverse()`
660 : * - `bondi_r()`
661 : * - `d_bondi_r()`
662 : * - `dyads()`
663 : * - `beta_worldtube_data()`
664 : * - `bondi_u_worldtube_data()`
665 : * - `bondi_w_worldtube_data()`
666 : * - `bondi_j_worldtube_data()`
667 : * - `dr_bondi_j()`
668 : * - `d2lambda_bondi_r()`
669 : * - `bondi_q_worldtube_data()`
670 : * - `bondi_h_worldtube_data()`
671 : * - `du_j_worldtube_data()`
672 : */
673 1 : void create_bondi_boundary_data(
674 : gsl::not_null<Variables<
675 : Tags::characteristic_worldtube_boundary_tags<Tags::BoundaryValue>>*>
676 : bondi_boundary_data,
677 : const tnsr::iaa<DataVector, 3>& phi, const tnsr::aa<DataVector, 3>& pi,
678 : const tnsr::aa<DataVector, 3>& spacetime_metric, double extraction_radius,
679 : size_t l_max);
680 :
681 : /*!
682 : * \brief Process the worldtube data from modal metric components and
683 : * derivatives to desired Bondi quantities, placing the result in the passed
684 : * `Variables`.
685 : *
686 : * \details
687 : * The mathematics are a bit complicated for all of the coordinate
688 : * transformations that are necessary to obtain the Bondi gauge quantities.
689 : * For full mathematical details, see the documentation for functions in
690 : * `BoundaryData.hpp` and \cite Barkett2019uae \cite Bishop1998uk.
691 : *
692 : * This function takes as input the full set of ADM metric data and its radial
693 : * and time derivatives on a two-dimensional surface of constant \f$r\f$ and
694 : * \f$t\f$ in numerical coordinates. This data must be provided as spherical
695 : * harmonic coefficients in the libsharp format. This data is provided in nine
696 : * `Tensor`s.
697 : *
698 : * Sufficient tags to provide full worldtube boundary data at a particular
699 : * time are set in `bondi_boundary_data`. In particular, the set of tags in
700 : * `Tags::characteristic_worldtube_boundary_tags` in the provided `Variables`
701 : * are assigned to the worldtube boundary values associated with the input
702 : * metric components.
703 : *
704 : * The majority of the mathematical transformations are implemented as a set of
705 : * individual cascaded functions below. The details of the manipulations that
706 : * are performed to the input data may be found in the individual functions
707 : * themselves, which are called in the following order:
708 : * - `trigonometric_functions_on_swsh_collocation()`
709 : * - `cartesian_to_spherical_coordinates_and_jacobians()`
710 : * - `cartesian_spatial_metric_and_derivatives_from_modes()`
711 : * - `cartesian_shift_and_derivatives_from_modes()`
712 : * - `cartesian_lapse_and_derivatives_from_modes()`
713 : * - `gh::phi()`
714 : * - `gr::time_derivative_of_spacetime_metric`
715 : * - `gr::spacetime_metric`
716 : * - `generalized_harmonic_quantities()`
717 : * - `worldtube_normal_and_derivatives()`
718 : * - `null_vector_l_and_derivatives()`
719 : * - `null_metric_and_derivative()`
720 : * - `dlambda_null_metric_and_inverse()`
721 : * - `bondi_r()`
722 : * - `d_bondi_r()`
723 : * - `dyads()`
724 : * - `beta_worldtube_data()`
725 : * - `bondi_u_worldtube_data()`
726 : * - `bondi_w_worldtube_data()`
727 : * - `bondi_j_worldtube_data()`
728 : * - `dr_bondi_j()`
729 : * - `d2lambda_bondi_r()`
730 : * - `bondi_q_worldtube_data()`
731 : * - `bondi_h_worldtube_data()`
732 : * - `du_j_worldtube_data()`
733 : */
734 1 : void create_bondi_boundary_data(
735 : gsl::not_null<Variables<
736 : Tags::characteristic_worldtube_boundary_tags<Tags::BoundaryValue>>*>
737 : bondi_boundary_data,
738 : const tnsr::ii<ComplexModalVector, 3>& spatial_metric_coefficients,
739 : const tnsr::ii<ComplexModalVector, 3>& dt_spatial_metric_coefficients,
740 : const tnsr::ii<ComplexModalVector, 3>& dr_spatial_metric_coefficients,
741 : const tnsr::I<ComplexModalVector, 3>& shift_coefficients,
742 : const tnsr::I<ComplexModalVector, 3>& dt_shift_coefficients,
743 : const tnsr::I<ComplexModalVector, 3>& dr_shift_coefficients,
744 : const Scalar<ComplexModalVector>& lapse_coefficients,
745 : const Scalar<ComplexModalVector>& dt_lapse_coefficients,
746 : const Scalar<ComplexModalVector>& dr_lapse_coefficients,
747 : double extraction_radius, size_t l_max);
748 :
749 : /*!
750 : * \brief Process the worldtube data from nodal metric components and
751 : * derivatives to desired Bondi quantities, placing the result in the passed
752 : * `Variables`.
753 : *
754 : * \details
755 : * The mathematics are a bit complicated for all of the coordinate
756 : * transformations that are necessary to obtain the Bondi gauge quantities.
757 : * For full mathematical details, see the documentation for functions in
758 : * `BoundaryData.hpp` and \cite Barkett2019uae \cite Bishop1998uk.
759 : *
760 : * This function takes as input the full set of ADM metric data and its radial
761 : * and time derivatives on a two-dimensional surface of constant \f$r\f$ and
762 : * \f$t\f$ in numerical coordinates. This data must be provided as values at
763 : * the collocation points compatible with the libsharp format. This data is
764 : * provided in nine `Tensor`s.
765 : *
766 : * Sufficient tags to provide full worldtube boundary data at a particular
767 : * time are set in `bondi_boundary_data`. In particular, the set of tags in
768 : * `Tags::characteristic_worldtube_boundary_tags` in the provided `Variables`
769 : * are assigned to the worldtube boundary values associated with the input
770 : * metric components.
771 : *
772 : * The majority of the mathematical transformations are implemented as a set of
773 : * individual cascaded functions below. The details of the manipulations that
774 : * are performed to the input data may be found in the individual functions
775 : * themselves, which are called in the following order:
776 : * - `trigonometric_functions_on_swsh_collocation()`
777 : * - `gh::phi()`
778 : * - `gr::time_derivative_of_spacetime_metric`
779 : * - `gr::spacetime_metric`
780 : * - `worldtube_normal_and_derivatives()`
781 : * - `null_vector_l_and_derivatives()`
782 : * - `cartesian_to_spherical_coordinates_and_jacobians()`
783 : * - `null_metric_and_derivative()`
784 : * - `dlambda_null_metric_and_inverse()`
785 : * - `bondi_r()`
786 : * - `d_bondi_r()`
787 : * - `dyads()`
788 : * - `beta_worldtube_data()`
789 : * - `bondi_u_worldtube_data()`
790 : * - `bondi_w_worldtube_data()`
791 : * - `bondi_j_worldtube_data()`
792 : * - `dr_bondi_j()`
793 : * - `d2lambda_bondi_r()`
794 : * - `bondi_q_worldtube_data()`
795 : * - `bondi_h_worldtube_data()`
796 : * - `du_j_worldtube_data()`
797 : */
798 1 : void create_bondi_boundary_data(
799 : gsl::not_null<Variables<
800 : Tags::characteristic_worldtube_boundary_tags<Tags::BoundaryValue>>*>
801 : bondi_boundary_data,
802 : const tnsr::ii<DataVector, 3>& cartesian_spatial_metric,
803 : const tnsr::ii<DataVector, 3>& cartesian_dt_spatial_metric,
804 : const tnsr::ii<DataVector, 3>& cartesian_dr_spatial_metric,
805 : const tnsr::I<DataVector, 3>& cartesian_shift,
806 : const tnsr::I<DataVector, 3>& cartesian_dt_shift,
807 : const tnsr::I<DataVector, 3>& cartesian_dr_shift,
808 : const Scalar<DataVector>& cartesian_lapse,
809 : const Scalar<DataVector>& cartesian_dt_lapse,
810 : const Scalar<DataVector>& cartesian_dr_lapse, double extraction_radius,
811 : size_t l_max);
812 :
813 : /*!
814 : * \brief Process the worldtube data from CurvedScalarWave quantities
815 : * to desired cce scalar quantities
816 : */
817 1 : void create_klein_gordon_boundary_data(
818 : gsl::not_null<Variables<Tags::characteristic_worldtube_boundary_tags<
819 : Tags::BoundaryValue, true>>*>
820 : bondi_boundary_data,
821 : const tnsr::i<DataVector, 3>& csw_phi, const Scalar<DataVector>& csw_pi,
822 : const Scalar<DataVector>& csw_psi, const Scalar<DataVector>& lapse,
823 : const tnsr::I<DataVector, 3>& shift);
824 :
825 : /*!
826 : * \brief Process the worldtube data from modal metric components and
827 : * derivatives with incorrectly normalized radial derivatives from an old
828 : * version of SpEC to desired Bondi quantities, placing the result in the passed
829 : * \ref DataBoxGroup.
830 : *
831 : * \details
832 : * The mathematics are a bit complicated for all of the coordinate
833 : * transformations that are necessary to obtain the Bondi gauge quantities.
834 : * For full mathematical details, see the documentation for functions in
835 : * `BoundaryData.hpp` and \cite Barkett2019uae \cite Bishop1998uk.
836 : *
837 : * This function takes as input the full set of ADM metric data and its radial
838 : * and time derivatives on a two-dimensional surface of constant \f$r\f$ and
839 : * \f$t\f$ in numerical coordinates. This data must be provided as spherical
840 : * harmonic coefficients in the libsharp format. This data is provided in nine
841 : * `Tensor`s.
842 : *
843 : * Sufficient tags to provide full worldtube boundary data at a particular
844 : * time are set in `bondi_boundary_data`. In particular, the set of tags in
845 : * `Tags::characteristic_worldtube_boundary_tags` in the provided \ref
846 : * DataBoxGroup are assigned to the worldtube boundary values associated with
847 : * the input metric components.
848 : *
849 : * The majority of the mathematical transformations are implemented as a set of
850 : * individual cascaded functions below. The details of the manipulations that
851 : * are performed to the input data may be found in the individual functions
852 : * themselves, which are called in the following order:
853 : * - `trigonometric_functions_on_swsh_collocation()`
854 : * - `cartesian_to_spherical_coordinates_and_jacobians()`
855 : * - `cartesian_spatial_metric_and_derivatives_from_unnormalized_spec_modes()`
856 : * - `cartesian_shift_and_derivatives_from_unnormalized_spec_modes()`
857 : * - `cartesian_lapse_and_derivatives_from_unnormalized_spec_modes()`
858 : * - `gh::phi()`
859 : * - `gr::time_derivative_of_spacetime_metric`
860 : * - `gr::spacetime_metric`
861 : * - `generalized_harmonic_quantities()`
862 : * - `worldtube_normal_and_derivatives()`
863 : * - `null_vector_l_and_derivatives()`
864 : * - `null_metric_and_derivative()`
865 : * - `dlambda_null_metric_and_inverse()`
866 : * - `bondi_r()`
867 : * - `d_bondi_r()`
868 : * - `dyads()`
869 : * - `beta_worldtube_data()`
870 : * - `bondi_u_worldtube_data()`
871 : * - `bondi_w_worldtube_data()`
872 : * - `bondi_j_worldtube_data()`
873 : * - `dr_bondi_j()`
874 : * - `d2lambda_bondi_r()`
875 : * - `bondi_q_worldtube_data()`
876 : * - `bondi_h_worldtube_data()`
877 : * - `du_j_worldtube_data()`
878 : */
879 1 : void create_bondi_boundary_data_from_unnormalized_spec_modes(
880 : gsl::not_null<Variables<
881 : Tags::characteristic_worldtube_boundary_tags<Tags::BoundaryValue>>*>
882 : bondi_boundary_data,
883 : const tnsr::ii<ComplexModalVector, 3>& spatial_metric_coefficients,
884 : const tnsr::ii<ComplexModalVector, 3>& dt_spatial_metric_coefficients,
885 : const tnsr::ii<ComplexModalVector, 3>& dr_spatial_metric_coefficients,
886 : const tnsr::I<ComplexModalVector, 3>& shift_coefficients,
887 : const tnsr::I<ComplexModalVector, 3>& dt_shift_coefficients,
888 : const tnsr::I<ComplexModalVector, 3>& dr_shift_coefficients,
889 : const Scalar<ComplexModalVector>& lapse_coefficients,
890 : const Scalar<ComplexModalVector>& dt_lapse_coefficients,
891 : const Scalar<ComplexModalVector>& dr_lapse_coefficients,
892 : double extraction_radius, size_t l_max);
893 : } // namespace Cce
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