Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <type_traits>
7 :
8 : #include "DataStructures/SpinWeighted.hpp" // IWYU pragma: keep
9 : #include "DataStructures/Tags.hpp"
10 : #include "DataStructures/Tags/TempTensor.hpp"
11 : #include "DataStructures/Tensor/Tensor.hpp"
12 : #include "Evolution/Systems/Cce/Tags.hpp" // IWYU pragma: keep
13 : #include "NumericalAlgorithms/Spectral/SwshTags.hpp"
14 : #include "Utilities/Gsl.hpp"
15 : #include "Utilities/TMPL.hpp"
16 :
17 : // IWYU pragma: no_forward_declare Cce::Tags::BondiBeta
18 : // IWYU pragma: no_forward_declare Cce::Tags::DuRDividedByR
19 : // IWYU pragma: no_forward_declare Cce::Tags::EthRDividedByR
20 : // IWYU pragma: no_forward_declare Cce::Tags::Exp2Beta
21 : // IWYU pragma: no_forward_declare Cce::Tags::BondiH
22 : // IWYU pragma: no_forward_declare Cce::Tags::BondiJ
23 : // IWYU pragma: no_forward_declare Cce::Tags::BondiJbar
24 : // IWYU pragma: no_forward_declare Cce::Tags::JbarQMinus2EthBeta
25 : // IWYU pragma: no_forward_declare Cce::Tags::BondiK
26 : // IWYU pragma: no_forward_declare Cce::Tags::OneMinusY
27 : // IWYU pragma: no_forward_declare Cce::Tags::BondiQ
28 : // IWYU pragma: no_forward_declare Cce::Tags::BondiR
29 : // IWYU pragma: no_forward_declare Cce::Tags::BondiU
30 : // IWYU pragma: no_forward_declare Cce::Tags::BondiUbar
31 : // IWYU pragma: no_forward_declare Cce::Tags::BondiW
32 : // IWYU pragma: no_forward_declare ::Tags::Multiplies
33 : // IWYU pragma: no_forward_declare Cce::Tags::Dy
34 : // IWYU pragma: no_forward_declare Cce::Tags::Integrand
35 : // IWYU pragma: no_forward_declare Cce::Tags::LinearFactor
36 : // IWYU pragma: no_forward_declare Cce::Tags::LinearFactorForConjugate
37 : // IWYU pragma: no_forward_declare Cce::Tags::PoleOfIntegrand
38 : // IWYU pragma: no_forward_declare Cce::Tags::RegularIntegrand
39 : // IWYU pragma: no_forward_declare Spectral::Swsh::Tags::Eth
40 : // IWYU pragma: no_forward_declare Spectral::Swsh::Tags::EthEth
41 : // IWYU pragma: no_forward_declare Spectral::Swsh::Tags::EthEthbar
42 : // IWYU pragma: no_forward_declare Spectral::Swsh::Tags::Ethbar
43 : // IWYU pragma: no_forward_declare Spectral::Swsh::Tags::EthbarEthbar
44 : // IWYU pragma: no_forward_declare Spectral::Swsh::Tags::Derivative
45 : // IWYU pragma: no_forward_declare Tags::TempTensor
46 : // IWYU pragma: no_forward_declare Tags::SpinWeighted
47 : // IWYU pragma: no_forward_declare SpinWeighted
48 : // IWYU pragma: no_forward_declare Tensor
49 :
50 : /// \cond
51 : class ComplexDataVector;
52 : /// \endcond
53 :
54 : namespace Cce {
55 :
56 : namespace detail {
57 : template <typename BondiVariable>
58 : struct integrand_terms_to_compute_for_bondi_variable_impl;
59 :
60 : // template specializations for the individual tags
61 : template <>
62 : struct integrand_terms_to_compute_for_bondi_variable_impl<Tags::BondiBeta> {
63 : using type = tmpl::list<Tags::Integrand<Tags::BondiBeta>>;
64 : };
65 : template <>
66 : struct integrand_terms_to_compute_for_bondi_variable_impl<Tags::BondiQ> {
67 : using type = tmpl::list<Tags::PoleOfIntegrand<Tags::BondiQ>,
68 : Tags::RegularIntegrand<Tags::BondiQ>>;
69 : };
70 : template <>
71 : struct integrand_terms_to_compute_for_bondi_variable_impl<Tags::BondiU> {
72 : using type = tmpl::list<Tags::Integrand<Tags::BondiU>>;
73 : };
74 : template <>
75 : struct integrand_terms_to_compute_for_bondi_variable_impl<Tags::BondiW> {
76 : using type = tmpl::list<Tags::PoleOfIntegrand<Tags::BondiW>,
77 : Tags::RegularIntegrand<Tags::BondiW>>;
78 : };
79 : template <>
80 : struct integrand_terms_to_compute_for_bondi_variable_impl<Tags::BondiH> {
81 : using type = tmpl::list<Tags::PoleOfIntegrand<Tags::BondiH>,
82 : Tags::RegularIntegrand<Tags::BondiH>,
83 : Tags::LinearFactor<Tags::BondiH>,
84 : Tags::LinearFactorForConjugate<Tags::BondiH>>;
85 : };
86 :
87 : template <>
88 : struct integrand_terms_to_compute_for_bondi_variable_impl<Tags::KleinGordonPi> {
89 : using type = tmpl::list<Tags::PoleOfIntegrand<Tags::KleinGordonPi>,
90 : Tags::RegularIntegrand<Tags::KleinGordonPi>>;
91 : };
92 :
93 : void klein_gordon_rhs_npsi1(
94 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> result,
95 : const SpinWeighted<ComplexDataVector, 1>& eth_beta,
96 : const SpinWeighted<ComplexDataVector, 1>& eth_kg_psi,
97 : const SpinWeighted<ComplexDataVector, 0>& eth_ethbar_kg_psi,
98 : const SpinWeighted<ComplexDataVector, 0>& bondi_k);
99 :
100 : void klein_gordon_rhs_npsi2(
101 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> result,
102 : const SpinWeighted<ComplexDataVector, 2>& j,
103 : const SpinWeighted<ComplexDataVector, 2>& eth_eth_kg_psi,
104 : const SpinWeighted<ComplexDataVector, 1>& eth_beta,
105 : const SpinWeighted<ComplexDataVector, 1>& eth_kg_psi,
106 : const SpinWeighted<ComplexDataVector, 1>& ethbar_j);
107 :
108 : void klein_gordon_rhs_npsi3(
109 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> result,
110 : const SpinWeighted<ComplexDataVector, 1>& eth_k,
111 : const SpinWeighted<ComplexDataVector, 1>& eth_kg_psi);
112 :
113 : void klein_gordon_rhs_npsi4_divided_by_one_minues_y_squared(
114 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> result,
115 : const SpinWeighted<ComplexDataVector, 1>& eth_kg_psi,
116 : const SpinWeighted<ComplexDataVector, 1>& dy_bondi_u,
117 : const SpinWeighted<ComplexDataVector, 0>& ethbar_u,
118 : const SpinWeighted<ComplexDataVector, 1>& bondi_u,
119 : const SpinWeighted<ComplexDataVector, 1>& eth_dy_kg_psi,
120 : const SpinWeighted<ComplexDataVector, 0>& dy_kg_psi,
121 : const SpinWeighted<ComplexDataVector, 0>& bondi_r,
122 : const SpinWeighted<ComplexDataVector, 1>& eth_r_divided_by_r);
123 :
124 : void klein_gordon_rhs_tau(
125 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> result,
126 : const SpinWeighted<ComplexDataVector, 0>& one_minus_y,
127 : const SpinWeighted<ComplexDataVector, 0>& dy_w,
128 : const SpinWeighted<ComplexDataVector, 0>& dy_kg_psi,
129 : const SpinWeighted<ComplexDataVector, 0>& dy_dy_kg_psi,
130 : const SpinWeighted<ComplexDataVector, 0>& bondi_w,
131 : const SpinWeighted<ComplexDataVector, 0>& bondi_r);
132 : } // namespace detail
133 :
134 : /// \brief A struct for providing a `tmpl::list` of integrand tags that need to
135 : /// be computed before integration can proceed for a given Bondi variable tag.
136 : template <typename BondiVariable>
137 1 : using integrand_terms_to_compute_for_bondi_variable =
138 : typename detail::integrand_terms_to_compute_for_bondi_variable_impl<
139 : BondiVariable>::type;
140 :
141 : /*!
142 : * \brief Computes one of the inputs for the integration of one of the
143 : * Characteristic hypersurface equations.
144 : *
145 : * \details The template argument must be one of the integrand-related prefix
146 : * tags templated on a Bondi quantity tag for which that integrand is required.
147 : * The relevant prefix tags are `Tags::Integrand`, `Tags::PoleOfIntegrand`,
148 : * `Tags::RegularIntegrand`, `Tags::LinearFactor`, and
149 : * `Tags::LinearFactorForConjugate`. The Bondi quantity tags that these tags may
150 : * wrap are `Tags::BondiBeta`, `Tags::BondiQ`, `Tags::BondiU`, `Tags::BondiW`,
151 : * and `Tags::BondiH`.
152 : *
153 : * The integrand terms which may be computed for a given Bondi variable are
154 : * enumerated in the type alias `integrand_terms_to_compute_for_bondi_variable`,
155 : * which takes as a single template argument the tag for which integrand terms
156 : * would be computed, and is a `tmpl::list` of the integrand terms needed.
157 : *
158 : * The resulting quantity is returned by `not_null` pointer, and the required
159 : * argument tags are given in `return_tags` and `argument_tags` type aliases,
160 : * where the `return_tags` are passed by `not_null` pointer (so include
161 : * temporary buffers) and the `argument_tags` are passed by const reference.
162 : *
163 : * Additional mathematical details for each of the computations can be found in
164 : * the template specializations of this struct. All of the specializations have
165 : * a static `apply` function which takes as arguments
166 : * `SpinWeighted<ComplexDataVector, N>`s for each of the Bondi arguments.
167 : */
168 : template <typename IntegrandTag>
169 1 : struct ComputeBondiIntegrand;
170 :
171 : /*!
172 : * \brief Computes the integrand (right-hand side) of the equation which
173 : * determines the radial (y) dependence of the Bondi quantity \f$\beta\f$.
174 : *
175 : * \details The quantity \f$\beta\f$ is defined via the Bondi form of the
176 : * metric:
177 : * \f[
178 : * ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
179 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
180 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
181 : * angular dyad \f$q^A\f$:
182 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A
183 : * \bar{q}^B.\f]
184 : * See \cite Bishop1997ik \cite Handmer2014qha for full details.
185 : *
186 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
187 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
188 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
189 : * the worldtube. The equation which determines \f$\beta\f$ on a surface of
190 : * constant \f$u\f$ given \f$J\f$ on the same surface is
191 : * \f[\partial_y (\beta) =
192 : * \frac{1}{8} (-1 + y) \left(\partial_y (J) \partial_y(\bar{J})
193 : * - \frac{(\partial_y (J \bar{J}))^2}{4 K^2}\right). \f]
194 : */
195 : template <>
196 1 : struct ComputeBondiIntegrand<Tags::Integrand<Tags::BondiBeta>> {
197 : public:
198 0 : using pre_swsh_derivative_tags =
199 : tmpl::list<Tags::Dy<Tags::BondiJ>, Tags::BondiJ>;
200 0 : using swsh_derivative_tags = tmpl::list<>;
201 0 : using integration_independent_tags = tmpl::list<Tags::OneMinusY>;
202 0 : using temporary_tags = tmpl::list<>;
203 :
204 0 : using return_tags = tmpl::append<tmpl::list<Tags::Integrand<Tags::BondiBeta>>,
205 : temporary_tags>;
206 0 : using argument_tags =
207 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
208 : integration_independent_tags>;
209 :
210 : template <typename... Args>
211 0 : static void apply(
212 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
213 : integrand_for_beta,
214 : const Args&... args) {
215 : apply_impl(make_not_null(&get(*integrand_for_beta)), get(args)...);
216 : }
217 :
218 : private:
219 0 : static void apply_impl(
220 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> integrand_for_beta,
221 : const SpinWeighted<ComplexDataVector, 2>& dy_j,
222 : const SpinWeighted<ComplexDataVector, 2>& j,
223 : const SpinWeighted<ComplexDataVector, 0>& one_minus_y);
224 : };
225 :
226 : /*!
227 : * \brief Computes the pole part of the integrand (right-hand side) of the
228 : * equation which determines the radial (y) dependence of the Bondi quantity
229 : * \f$Q\f$.
230 : *
231 : * \details The quantity \f$Q\f$ is defined via the Bondi form of the metric:
232 : * \f[ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
233 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
234 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
235 : * angular dyad \f$q^A\f$:
236 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A \bar{q}^B,\f]
237 : * and \f$Q\f$ is defined as a supplemental variable for radial integration of
238 : * \f$U\f$:
239 : * \f[ Q_A = r^2 e^{-2\beta} h_{AB} \partial_r U^B\f]
240 : * and \f$Q = Q_A q^A\f$. See \cite Bishop1997ik \cite Handmer2014qha for full
241 : * details.
242 : *
243 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
244 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
245 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
246 : * the worldtube. The equation which determines \f$Q\f$ on a surface of constant
247 : * \f$u\f$ given \f$J\f$ and \f$\beta\f$ on the same surface is written as
248 : * \f[(1 - y) \partial_y Q + 2 Q = A_Q + (1 - y) B_Q.\f]
249 : * We refer to \f$A_Q\f$ as the "pole part" of the integrand and \f$B_Q\f$
250 : * as the "regular part". The pole part is computed by this function, and has
251 : * the expression
252 : * \f[A_Q = -4 \eth \beta.\f]
253 : */
254 : template <>
255 1 : struct ComputeBondiIntegrand<Tags::PoleOfIntegrand<Tags::BondiQ>> {
256 : public:
257 0 : using pre_swsh_derivative_tags = tmpl::list<>;
258 0 : using swsh_derivative_tags =
259 : tmpl::list<Spectral::Swsh::Tags::Derivative<Tags::BondiBeta,
260 : Spectral::Swsh::Tags::Eth>>;
261 0 : using integration_independent_tags = tmpl::list<>;
262 0 : using temporary_tags = tmpl::list<>;
263 :
264 0 : using return_tags =
265 : tmpl::append<tmpl::list<Tags::PoleOfIntegrand<Tags::BondiQ>>,
266 : temporary_tags>;
267 0 : using argument_tags =
268 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
269 : integration_independent_tags>;
270 :
271 : template <typename... Args>
272 0 : static void apply(
273 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*>
274 : pole_of_integrand_for_q,
275 : const Args&... args) {
276 : apply_impl(make_not_null(&get(*pole_of_integrand_for_q)), get(args)...);
277 : }
278 :
279 : private:
280 0 : static void apply_impl(gsl::not_null<SpinWeighted<ComplexDataVector, 1>*>
281 : pole_of_integrand_for_q,
282 : const SpinWeighted<ComplexDataVector, 1>& eth_beta);
283 : };
284 :
285 : /*!
286 : * \brief Computes the regular part of the integrand (right-hand side) of the
287 : * equation which determines the radial (y) dependence of the Bondi quantity
288 : * \f$Q\f$.
289 : *
290 : * \details The quantity \f$Q\f$ is defined via the Bondi form of the metric:
291 : * \f[ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
292 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
293 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
294 : * angular dyad \f$q^A\f$:
295 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A \bar{q}^B,\f]
296 : * and \f$Q\f$ is defined as a supplemental variable for radial integration of
297 : * \f$U\f$:
298 : * \f[ Q_A = r^2 e^{-2\beta} h_{AB} \partial_r U^B\f]
299 : * and \f$Q = Q_A q^A\f$. See \cite Bishop1997ik \cite Handmer2014qha for
300 : * full details.
301 : *
302 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
303 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
304 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
305 : * the worldtube. The equation which determines \f$Q\f$ on a surface of constant
306 : * \f$u\f$ given \f$J\f$ and \f$\beta\f$ on the same surface is written as
307 : * \f[(1 - y) \partial_y Q + 2 Q = A_Q + (1 - y) B_Q. \f]
308 : * We refer to \f$A_Q\f$ as the "pole part" of the integrand and \f$B_Q\f$ as
309 : * the "regular part". The regular part is computed by this function, and has
310 : * the expression
311 : * \f[ B_Q = - \left(2 \mathcal{A}_Q + \frac{2
312 : * \bar{\mathcal{A}_Q} J}{K} - 2 \partial_y (\eth (\beta)) +
313 : * \frac{\partial_y (\bar{\eth} (J))}{K}\right), \f]
314 : * where
315 : * \f[ \mathcal{A}_Q = - \tfrac{1}{4} \eth (\bar{J} \partial_y (J)) +
316 : * \tfrac{1}{4} J \partial_y (\eth (\bar{J})) - \tfrac{1}{4} \eth (\bar{J})
317 : * \partial_y (J) + \frac{\eth (J \bar{J}) \partial_y (J \bar{J})}{8 K^2} -
318 : * \frac{\bar{J} \eth (R) \partial_y (J)}{4 R}. \f].
319 : */
320 : template <>
321 1 : struct ComputeBondiIntegrand<Tags::RegularIntegrand<Tags::BondiQ>> {
322 : public:
323 0 : using pre_swsh_derivative_tags =
324 : tmpl::list<Tags::Dy<Tags::BondiBeta>, Tags::Dy<Tags::BondiJ>,
325 : Tags::BondiJ>;
326 0 : using swsh_derivative_tags = tmpl::list<
327 : Spectral::Swsh::Tags::Derivative<Tags::Dy<Tags::BondiBeta>,
328 : Spectral::Swsh::Tags::Eth>,
329 : Spectral::Swsh::Tags::Derivative<
330 : ::Tags::Multiplies<Tags::BondiJ, Tags::BondiJbar>,
331 : Spectral::Swsh::Tags::Eth>,
332 : Spectral::Swsh::Tags::Derivative<
333 : ::Tags::Multiplies<Tags::BondiJbar, Tags::Dy<Tags::BondiJ>>,
334 : Spectral::Swsh::Tags::Eth>,
335 : Spectral::Swsh::Tags::Derivative<Tags::Dy<Tags::BondiJ>,
336 : Spectral::Swsh::Tags::Ethbar>,
337 : Spectral::Swsh::Tags::Derivative<Tags::BondiJ,
338 : Spectral::Swsh::Tags::Ethbar>>;
339 0 : using integration_independent_tags =
340 : tmpl::list<Tags::EthRDividedByR, Tags::BondiK>;
341 0 : using temporary_tags =
342 : tmpl::list<::Tags::SpinWeighted<::Tags::TempScalar<0, ComplexDataVector>,
343 : std::integral_constant<int, 1>>>;
344 :
345 0 : using return_tags =
346 : tmpl::append<tmpl::list<Tags::RegularIntegrand<Tags::BondiQ>>,
347 : temporary_tags>;
348 0 : using argument_tags =
349 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
350 : integration_independent_tags>;
351 :
352 : template <typename... Args>
353 0 : static void apply(
354 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*>
355 : regular_integrand_for_q,
356 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*>
357 : script_aq,
358 : const Args&... args) {
359 : apply_impl(make_not_null(&get(*regular_integrand_for_q)),
360 : make_not_null(&get(*script_aq)), get(args)...);
361 : }
362 :
363 : private:
364 0 : static void apply_impl(
365 : gsl::not_null<SpinWeighted<ComplexDataVector, 1>*>
366 : regular_integrand_for_q,
367 : gsl::not_null<SpinWeighted<ComplexDataVector, 1>*> script_aq,
368 : const SpinWeighted<ComplexDataVector, 0>& dy_beta,
369 : const SpinWeighted<ComplexDataVector, 2>& dy_j,
370 : const SpinWeighted<ComplexDataVector, 2>& j,
371 : const SpinWeighted<ComplexDataVector, 1>& eth_dy_beta,
372 : const SpinWeighted<ComplexDataVector, 1>& eth_j_jbar,
373 : const SpinWeighted<ComplexDataVector, 1>& eth_jbar_dy_j,
374 : const SpinWeighted<ComplexDataVector, 1>& ethbar_dy_j,
375 : const SpinWeighted<ComplexDataVector, 1>& ethbar_j,
376 : const SpinWeighted<ComplexDataVector, 1>& eth_r_divided_by_r,
377 : const SpinWeighted<ComplexDataVector, 0>& k);
378 : };
379 :
380 : /*!
381 : * \brief Computes the integrand (right-hand side) of the equation which
382 : * determines the radial (y) dependence of the Bondi quantity \f$U\f$.
383 : *
384 : * \details The quantity \f$U\f$ is defined via the Bondi form of the metric:
385 : * \f[ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
386 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
387 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
388 : * angular dyad \f$q^A\f$:
389 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A \bar{q}^B,\f]
390 : * and \f$Q\f$ is defined as a supplemental variable for radial integration of
391 : * \f$U\f$:
392 : * \f[ Q_A = r^2 e^{-2\beta} h_{AB} \partial_r U^B\f]
393 : * and \f$U = U_A q^A\f$. See \cite Bishop1997ik \cite Handmer2014qha for full
394 : * details.
395 : *
396 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
397 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
398 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
399 : * the worldtube. The equation which determines \f$U\f$ on a surface of constant
400 : * \f$u\f$ given \f$J\f$, \f$\beta\f$, and \f$Q\f$ on the same surface is
401 : * written as
402 : * \f[\partial_y U = \frac{e^{2\beta}}{2 R} (K Q - J \bar{Q}). \f]
403 : */
404 : template <>
405 1 : struct ComputeBondiIntegrand<Tags::Integrand<Tags::BondiU>> {
406 : public:
407 0 : using pre_swsh_derivative_tags =
408 : tmpl::list<Tags::Exp2Beta, Tags::BondiJ, Tags::BondiQ>;
409 0 : using swsh_derivative_tags = tmpl::list<>;
410 0 : using integration_independent_tags = tmpl::list<Tags::BondiK, Tags::BondiR>;
411 0 : using temporary_tags = tmpl::list<>;
412 :
413 0 : using return_tags =
414 : tmpl::append<tmpl::list<Tags::Integrand<Tags::BondiU>>, temporary_tags>;
415 0 : using argument_tags =
416 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
417 : integration_independent_tags>;
418 :
419 : template <typename... Args>
420 0 : static void apply(
421 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*>
422 : regular_integrand_for_u,
423 : const Args&... args) {
424 : apply_impl(make_not_null(&get(*regular_integrand_for_u)), get(args)...);
425 : }
426 :
427 : private:
428 0 : static void apply_impl(gsl::not_null<SpinWeighted<ComplexDataVector, 1>*>
429 : regular_integrand_for_u,
430 : const SpinWeighted<ComplexDataVector, 0>& exp_2_beta,
431 : const SpinWeighted<ComplexDataVector, 2>& j,
432 : const SpinWeighted<ComplexDataVector, 1>& q,
433 : const SpinWeighted<ComplexDataVector, 0>& k,
434 : const SpinWeighted<ComplexDataVector, 0>& r);
435 : };
436 :
437 : /*!
438 : * \brief Computes the pole part of the integrand (right-hand side) of the
439 : * equation which determines the radial (y) dependence of the Bondi quantity
440 : * \f$W\f$.
441 : *
442 : * \details The quantity \f$W\f$ is defined via the Bondi form of the metric:
443 : * \f[ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
444 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
445 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
446 : * angular dyad \f$q^A\f$:
447 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A \bar{q}^B.\f]
448 : * See \cite Bishop1997ik \cite Handmer2014qha for full details.
449 : *
450 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
451 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
452 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
453 : * the worldtube. The equation which determines \f$W\f$ on a surface of constant
454 : * \f$u\f$ given \f$J\f$,\f$\beta\f$, \f$Q\f$, and \f$U\f$ on the same surface
455 : * is written as
456 : * \f[(1 - y) \partial_y W + 2 W = A_W + (1 - y) B_W.\f] We refer
457 : * to \f$A_W\f$ as the "pole part" of the integrand and \f$B_W\f$ as the
458 : * "regular part". The pole part is computed by this function, and has the
459 : * expression
460 : * \f[A_W = \eth (\bar{U}) + \bar{\eth} (U).\f]
461 : */
462 : template <>
463 1 : struct ComputeBondiIntegrand<Tags::PoleOfIntegrand<Tags::BondiW>> {
464 : public:
465 0 : using pre_swsh_derivative_tags = tmpl::list<>;
466 0 : using swsh_derivative_tags = tmpl::list<Spectral::Swsh::Tags::Derivative<
467 : Tags::BondiU, Spectral::Swsh::Tags::Ethbar>>;
468 0 : using integration_independent_tags = tmpl::list<>;
469 0 : using temporary_tags = tmpl::list<>;
470 :
471 0 : using return_tags =
472 : tmpl::append<tmpl::list<Tags::PoleOfIntegrand<Tags::BondiW>>,
473 : temporary_tags>;
474 0 : using argument_tags =
475 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
476 : integration_independent_tags>;
477 :
478 : template <typename... Args>
479 0 : static void apply(
480 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
481 : pole_of_integrand_for_w,
482 : const Args&... args) {
483 : apply_impl(make_not_null(&get(*pole_of_integrand_for_w)), get(args)...);
484 : }
485 :
486 : private:
487 0 : static void apply_impl(gsl::not_null<SpinWeighted<ComplexDataVector, 0>*>
488 : pole_of_integrand_for_w,
489 : const SpinWeighted<ComplexDataVector, 0>& ethbar_u);
490 : };
491 :
492 : /*!
493 : * \brief Computes the regular part of the integrand (right-hand side) of the
494 : * equation which determines the radial (y) dependence of the Bondi quantity
495 : * \f$W\f$.
496 : *
497 : * \details The quantity \f$W\f$ is defined via the Bondi form of the metric:
498 : * \f[ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
499 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
500 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
501 : * angular dyad \f$q^A\f$:
502 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A \bar{q}^B,\f]
503 : * See \cite Bishop1997ik \cite Handmer2014qha for full details.
504 : *
505 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
506 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
507 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
508 : * the worldtube. The equation which determines \f$W\f$ on a surface of constant
509 : * \f$u\f$ given \f$J\f$, \f$\beta\f$, \f$Q\f$, \f$U\f$ on the same surface is
510 : * written as
511 : * \f[(1 - y) \partial_y W + 2 W = A_W + (1 - y) B_W. \f]
512 : * We refer to \f$A_W\f$ as the "pole part" of the integrand and \f$B_W\f$ as
513 : * the "regular part". The regular part is computed by this function, and has
514 : * the expression
515 : * \f[ B_W = \tfrac{1}{4} \partial_y (\eth (\bar{U})) + \tfrac{1}{4} \partial_y
516 : * (\bar{\eth} (U)) - \frac{1}{2 R} + \frac{e^{2 \beta} (\mathcal{A}_W +
517 : * \bar{\mathcal{A}_W})}{4 R}, \f]
518 : * where
519 : * \f{align*}
520 : * \mathcal{A}_W =& - \eth (\beta) \eth (\bar{J}) + \tfrac{1}{2} \bar{\eth}
521 : * (\bar{\eth} (J)) + 2 \bar{\eth} (\beta) \bar{\eth} (J) + (\bar{\eth}
522 : * (\beta))^2 J + \bar{\eth}
523 : * (\bar{\eth} (\beta)) J + \frac{\eth (J \bar{J}) \bar{\eth} (J \bar{J})}{8
524 : * K^3} + \frac{1}{2 K} - \frac{\eth (\bar{\eth} (J \bar{J}))}{8 K} -
525 : * \frac{\eth (J
526 : * \bar{J}) \bar{\eth} (\beta)}{2 K} \nonumber \\
527 : * &- \frac{\eth (\bar{J}) \bar{\eth} (J)}{4 K} - \frac{\eth (\bar{\eth} (J))
528 : * \bar{J}}{4 K} + \tfrac{1}{2} K - \eth (\bar{\eth} (\beta)) K - \eth
529 : * (\beta) \bar{\eth} (\beta) K + \tfrac{1}{4} (- K Q \bar{Q} + J \bar{Q}^2).
530 : * \f}
531 : */
532 : template <>
533 1 : struct ComputeBondiIntegrand<Tags::RegularIntegrand<Tags::BondiW>> {
534 : public:
535 0 : using pre_swsh_derivative_tags =
536 : tmpl::list<Tags::Dy<Tags::BondiU>, Tags::Exp2Beta, Tags::BondiJ,
537 : Tags::BondiQ>;
538 0 : using swsh_derivative_tags = tmpl::list<
539 : Spectral::Swsh::Tags::Derivative<Tags::BondiBeta,
540 : Spectral::Swsh::Tags::Eth>,
541 : Spectral::Swsh::Tags::Derivative<Tags::BondiBeta,
542 : Spectral::Swsh::Tags::EthEth>,
543 : Spectral::Swsh::Tags::Derivative<Tags::BondiBeta,
544 : Spectral::Swsh::Tags::EthEthbar>,
545 : Spectral::Swsh::Tags::Derivative<
546 : Spectral::Swsh::Tags::Derivative<Tags::BondiJ,
547 : Spectral::Swsh::Tags::Ethbar>,
548 : Spectral::Swsh::Tags::Eth>,
549 : Spectral::Swsh::Tags::Derivative<
550 : ::Tags::Multiplies<Tags::BondiJ, Tags::BondiJbar>,
551 : Spectral::Swsh::Tags::EthEthbar>,
552 : Spectral::Swsh::Tags::Derivative<
553 : ::Tags::Multiplies<Tags::BondiJ, Tags::BondiJbar>,
554 : Spectral::Swsh::Tags::Eth>,
555 : Spectral::Swsh::Tags::Derivative<Tags::Dy<Tags::BondiU>,
556 : Spectral::Swsh::Tags::Ethbar>,
557 : Spectral::Swsh::Tags::Derivative<Tags::BondiJ,
558 : Spectral::Swsh::Tags::EthbarEthbar>,
559 : Spectral::Swsh::Tags::Derivative<Tags::BondiJ,
560 : Spectral::Swsh::Tags::Ethbar>>;
561 0 : using integration_independent_tags =
562 : tmpl::list<Tags::EthRDividedByR, Tags::BondiK, Tags::BondiR>;
563 0 : using temporary_tags =
564 : tmpl::list<::Tags::SpinWeighted<::Tags::TempScalar<0, ComplexDataVector>,
565 : std::integral_constant<int, 0>>>;
566 :
567 0 : using return_tags =
568 : tmpl::append<tmpl::list<Tags::RegularIntegrand<Tags::BondiW>>,
569 : temporary_tags>;
570 0 : using argument_tags =
571 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
572 : integration_independent_tags>;
573 :
574 : template <typename... Args>
575 0 : static void apply(
576 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
577 : regular_integrand_for_w,
578 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
579 : script_av,
580 : const Args&... args) {
581 : apply_impl(make_not_null(&get(*regular_integrand_for_w)),
582 : make_not_null(&get(*script_av)), get(args)...);
583 : }
584 :
585 : private:
586 0 : static void apply_impl(
587 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*>
588 : regular_integrand_for_w,
589 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> script_av,
590 : const SpinWeighted<ComplexDataVector, 1>& dy_u,
591 : const SpinWeighted<ComplexDataVector, 0>& exp_2_beta,
592 : const SpinWeighted<ComplexDataVector, 2>& j,
593 : const SpinWeighted<ComplexDataVector, 1>& q,
594 : const SpinWeighted<ComplexDataVector, 1>& eth_beta,
595 : const SpinWeighted<ComplexDataVector, 2>& eth_eth_beta,
596 : const SpinWeighted<ComplexDataVector, 0>& eth_ethbar_beta,
597 : const SpinWeighted<ComplexDataVector, 2>& eth_ethbar_j,
598 : const SpinWeighted<ComplexDataVector, 0>& eth_ethbar_j_jbar,
599 : const SpinWeighted<ComplexDataVector, 1>& eth_j_jbar,
600 : const SpinWeighted<ComplexDataVector, 0>& ethbar_dy_u,
601 : const SpinWeighted<ComplexDataVector, 0>& ethbar_ethbar_j,
602 : const SpinWeighted<ComplexDataVector, 1>& ethbar_j,
603 : const SpinWeighted<ComplexDataVector, 1>& eth_r_divided_by_r,
604 : const SpinWeighted<ComplexDataVector, 0>& k,
605 : const SpinWeighted<ComplexDataVector, 0>& r);
606 : };
607 :
608 : /*!
609 : * \brief Computes the pole part of the integrand (right-hand side) of the
610 : * equation which determines the radial (y) dependence of the Bondi quantity
611 : * \f$H\f$.
612 : *
613 : * \details The quantity \f$H \equiv \partial_u J\f$ (evaluated at constant y)
614 : * is defined via the Bondi form of the metric:
615 : * \f[ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
616 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
617 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
618 : * angular dyad \f$q^A\f$:
619 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A \bar{q}^B.\f]
620 : * See \cite Bishop1997ik \cite Handmer2014qha for full details.
621 : *
622 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
623 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
624 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
625 : * the worldtube. The equation which determines \f$W\f$ on a surface of constant
626 : * \f$u\f$ given \f$J\f$,\f$\beta\f$, \f$Q\f$, \f$U\f$, and \f$W\f$ on the same
627 : * surface is written as
628 : * \f[(1 - y) \partial_y H + H + (1 - y)(\mathcal{D}_J H
629 : * + \bar{\mathcal{D}}_J \bar{H}) = A_J + (1 - y) B_J.\f]
630 : *
631 : * We refer to \f$A_J\f$ as the "pole part" of the integrand
632 : * and \f$B_J\f$ as the "regular part". The pole part is computed by this
633 : * function, and has the expression
634 : * \f{align*}
635 : * A_J =& - \tfrac{1}{2} \eth (J \bar{U}) - \eth (\bar{U}) J - \tfrac{1}{2}
636 : * \bar{\eth} (U) J - \eth (U) K - \tfrac{1}{2} (\bar{\eth} (J) U) + 2 J W
637 : * \f}
638 : */
639 : template <>
640 1 : struct ComputeBondiIntegrand<Tags::PoleOfIntegrand<Tags::BondiH>> {
641 : public:
642 0 : using pre_swsh_derivative_tags =
643 : tmpl::list<Tags::BondiJ, Tags::BondiU, Tags::BondiW>;
644 0 : using swsh_derivative_tags = tmpl::list<
645 : Spectral::Swsh::Tags::Derivative<Tags::BondiU, Spectral::Swsh::Tags::Eth>,
646 : Spectral::Swsh::Tags::Derivative<Tags::BondiJ,
647 : Spectral::Swsh::Tags::Ethbar>,
648 : Spectral::Swsh::Tags::Derivative<
649 : ::Tags::Multiplies<Tags::BondiJbar, Tags::BondiU>,
650 : Spectral::Swsh::Tags::Ethbar>,
651 : Spectral::Swsh::Tags::Derivative<Tags::BondiU,
652 : Spectral::Swsh::Tags::Ethbar>>;
653 0 : using integration_independent_tags = tmpl::list<Tags::BondiK>;
654 0 : using temporary_tags = tmpl::list<>;
655 :
656 0 : using return_tags =
657 : tmpl::append<tmpl::list<Tags::PoleOfIntegrand<Tags::BondiH>>,
658 : temporary_tags>;
659 0 : using argument_tags =
660 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
661 : integration_independent_tags>;
662 :
663 : template <typename... Args>
664 0 : static void apply(
665 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*>
666 : pole_of_integrand_for_h,
667 : const Args&... args) {
668 : apply_impl(make_not_null(&get(*pole_of_integrand_for_h)), get(args)...);
669 : }
670 :
671 : private:
672 0 : static void apply_impl(
673 : gsl::not_null<SpinWeighted<ComplexDataVector, 2>*>
674 : pole_of_integrand_for_h,
675 : const SpinWeighted<ComplexDataVector, 2>& j,
676 : const SpinWeighted<ComplexDataVector, 1>& u,
677 : const SpinWeighted<ComplexDataVector, 0>& w,
678 : const SpinWeighted<ComplexDataVector, 2>& eth_u,
679 : const SpinWeighted<ComplexDataVector, 1>& ethbar_j,
680 : const SpinWeighted<ComplexDataVector, -2>& ethbar_jbar_u,
681 : const SpinWeighted<ComplexDataVector, 0>& ethbar_u,
682 : const SpinWeighted<ComplexDataVector, 0>& k);
683 : };
684 :
685 : /*!
686 : * \brief Computes the pole part of the integrand (right-hand side) of the
687 : * equation which determines the radial (y) dependence of the Bondi quantity
688 : * \f$H\f$.
689 : *
690 : * \details The quantity \f$H \equiv \partial_u J\f$ (evaluated at constant y)
691 : * is defined via the Bondi form of the metric:
692 : * \f[ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
693 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
694 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
695 : * angular dyad \f$q^A\f$:
696 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A \bar{q}^B.\f]
697 : * See \cite Bishop1997ik \cite Handmer2014qha for full details.
698 : *
699 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
700 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
701 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
702 : * the worldtube. The equation which determines \f$H\f$ on a surface of constant
703 : * \f$u\f$ given \f$J\f$,\f$\beta\f$, \f$Q\f$, \f$U\f$, and \f$W\f$ on the same
704 : * surface is written as
705 : * \f[(1 - y) \partial_y H + H + (1 - y)(\mathcal{D}_J H + \bar{\mathcal{D}}_J
706 : * \bar{H}) = A_J + (1 - y) B_J.\f]
707 : * We refer to \f$A_J\f$ as the "pole part" of the integrand
708 : * and \f$B_J\f$ as the "regular part". The pole part is computed by this
709 : * function, and has the expression
710 : * \f{align*}
711 : * B_J =& -\tfrac{1}{2} \left(\eth(\partial_y (J) \bar{U}) + \partial_y
712 : * (\bar{\eth} (J)) U \right) + J (\mathcal{B}_J + \bar{\mathcal{B}}_J) \notag\\
713 : * &+ \frac{e^{2 \beta}}{2 R} \left(\mathcal{C}_J + \eth (\eth (\beta)) -
714 : * \tfrac{1}{2} \eth (Q) - (\mathcal{A}_J + \bar{\mathcal{A}_J}) J +
715 : * \frac{\bar{\mathcal{C}_J} J^2}{K^2} + \frac{\eth (J (-2 \bar{\eth} (\beta) +
716 : * \bar{Q}))}{4 K} - \frac{\eth (\bar{Q}) J}{4 K} + (\eth (\beta) -
717 : * \tfrac{1}{2} Q)^2\right) \notag\\
718 : * &- \partial_y (J) \left(\frac{\eth (U) \bar{J}}{2 K} - \tfrac{1}{2}
719 : * \bar{\eth} (\bar{U}) J K + \tfrac{1}{4} (\eth (\bar{U}) - \bar{\eth} (U))
720 : * K^2 + \frac{1}{2} \frac{\eth (R) \bar{U}}{R} - \frac{1}{2}
721 : * W\right)\notag\\
722 : * &+ \partial_y (\bar{J}) \left(- \tfrac{1}{4} (- \eth (\bar{U}) + \bar{\eth}
723 : * (U)) J^2 + \eth (U) J \left(- \frac{1}{2 K} + \tfrac{1}{2}
724 : * K\right)\right)\notag\\
725 : * &+ (1 - y) \bigg[\frac{1}{2} \left(- \frac{\partial_y (J)}{R} + \frac{2
726 : * \partial_{u} (R) \partial_y (\partial_y (J))}{R} + \partial_y
727 : * (\partial_y (J)) W\right) + \partial_y (J) \left(\tfrac{1}{2} \partial_y (W)
728 : * + \frac{1}{2 R}\right)\bigg]\notag\\
729 : * &+ (1 - y)^2 \bigg[ \frac{\partial_y (\partial_y (J)) }{4 R} \bigg],
730 : * \f}
731 : * where
732 : * \f{align*}
733 : * \mathcal{A}_J =& \tfrac{1}{4} \eth (\eth (\bar{J})) - \frac{1}{4 K^3} -
734 : * \frac{\eth (\bar{\eth} (J \bar{J})) - (\eth (\bar{\eth} (\bar{J})) - 4
735 : \bar{J})
736 : * J}{16 K^3} + \frac{3}{4 K} - \frac{\eth (\bar{\eth} (\beta))}{4 K} \notag\\
737 : * &- \frac{\eth (\bar{\eth} (J)) \bar{J} (1 - \frac{1}{4 K^2})}{4 K} +
738 : * \tfrac{1}{2} \eth (\bar{J}) \left(\eth (\beta) + \frac{\bar{\eth} (J \bar{J})
739 : * J}{4 K^3} - \frac{\bar{\eth} (J) (-1 + 2 K^2)}{4 K^3} - \tfrac{1}{2}
740 : * Q\right)\\
741 : * \mathcal{B}_J =& - \frac{\eth (U) \bar{J} \partial_y (J \bar{J})}{4 K} +
742 : * \tfrac{1}{2} \partial_y (W) + \frac{1}{4 R} + \tfrac{1}{4} \bar{\eth} (J)
743 : * \partial_y (\bar{J}) U - \frac{\bar{\eth} (J \bar{J}) \partial_y (J \bar{J})
744 : * U}{8 K^2} \notag\\&- \tfrac{1}{4} J \partial_y (\eth (\bar{J})) \bar{U} +
745 : * \tfrac{1}{4} (\eth (J \partial_y (\bar{J})) + \frac{J \eth (R)
746 : * \partial_y(\bar{J})}{R}) \bar{U} \\
747 : * &+ (1 - y) \bigg[ \frac{\mathcal{D}_J \partial_{u} (R)
748 : * \partial_y (J)}{R} - \tfrac{1}{4} \partial_y (J) \partial_y (\bar{J}) W +
749 : * \frac{(\partial_y (J \bar{J}))^2 W}{16 K^2} \bigg] \\
750 : * &+ (1 - y)^2 \bigg[ - \frac{\partial_y (J) \partial_y (\bar{J})}{8 R} +
751 : * \frac{(\partial_y (J \bar{J}))^2}{32 K^2 R} \bigg]\\
752 : * \mathcal{C}_J =& \tfrac{1}{2} \bar{\eth} (J) K (\eth (\beta) - \tfrac{1}{2}
753 : * Q)\\ \mathcal{D}_J =& \tfrac{1}{4} \left(-2 \partial_y (\bar{J}) +
754 : * \frac{\bar{J} \partial_y (J \bar{J})}{K^2}\right)
755 : * \f}
756 : */
757 : template <>
758 1 : struct ComputeBondiIntegrand<Tags::RegularIntegrand<Tags::BondiH>> {
759 : public:
760 0 : using pre_swsh_derivative_tags =
761 : tmpl::list<Tags::Dy<Tags::Dy<Tags::BondiJ>>, Tags::Dy<Tags::BondiJ>,
762 : Tags::Dy<Tags::BondiW>, Tags::Exp2Beta, Tags::BondiJ,
763 : Tags::BondiQ, Tags::BondiU, Tags::BondiW>;
764 0 : using swsh_derivative_tags = tmpl::list<
765 : Spectral::Swsh::Tags::Derivative<Tags::BondiBeta,
766 : Spectral::Swsh::Tags::Eth>,
767 : Spectral::Swsh::Tags::Derivative<Tags::BondiBeta,
768 : Spectral::Swsh::Tags::EthEth>,
769 : Spectral::Swsh::Tags::Derivative<Tags::BondiBeta,
770 : Spectral::Swsh::Tags::EthEthbar>,
771 : Spectral::Swsh::Tags::Derivative<
772 : Spectral::Swsh::Tags::Derivative<Tags::BondiJ,
773 : Spectral::Swsh::Tags::Ethbar>,
774 : Spectral::Swsh::Tags::Eth>,
775 : Spectral::Swsh::Tags::Derivative<
776 : ::Tags::Multiplies<Tags::BondiJ, Tags::BondiJbar>,
777 : Spectral::Swsh::Tags::EthEthbar>,
778 : Spectral::Swsh::Tags::Derivative<
779 : ::Tags::Multiplies<Tags::BondiJ, Tags::BondiJbar>,
780 : Spectral::Swsh::Tags::Eth>,
781 : Spectral::Swsh::Tags::Derivative<Tags::BondiQ, Spectral::Swsh::Tags::Eth>,
782 : Spectral::Swsh::Tags::Derivative<Tags::BondiU, Spectral::Swsh::Tags::Eth>,
783 : Spectral::Swsh::Tags::Derivative<
784 : ::Tags::Multiplies<Tags::BondiUbar, Tags::Dy<Tags::BondiJ>>,
785 : Spectral::Swsh::Tags::Eth>,
786 : Spectral::Swsh::Tags::Derivative<Tags::Dy<Tags::BondiJ>,
787 : Spectral::Swsh::Tags::Ethbar>,
788 : Spectral::Swsh::Tags::Derivative<Tags::BondiJ,
789 : Spectral::Swsh::Tags::EthbarEthbar>,
790 : Spectral::Swsh::Tags::Derivative<Tags::BondiJ,
791 : Spectral::Swsh::Tags::Ethbar>,
792 : Spectral::Swsh::Tags::Derivative<
793 : ::Tags::Multiplies<Tags::BondiJbar, Tags::Dy<Tags::BondiJ>>,
794 : Spectral::Swsh::Tags::Ethbar>,
795 : Spectral::Swsh::Tags::Derivative<Tags::JbarQMinus2EthBeta,
796 : Spectral::Swsh::Tags::Ethbar>,
797 : Spectral::Swsh::Tags::Derivative<Tags::BondiQ,
798 : Spectral::Swsh::Tags::Ethbar>,
799 : Spectral::Swsh::Tags::Derivative<Tags::BondiU,
800 : Spectral::Swsh::Tags::Ethbar>>;
801 0 : using integration_independent_tags =
802 : tmpl::list<Tags::DuRDividedByR, Tags::EthRDividedByR, Tags::BondiK,
803 : Tags::OneMinusY, Tags::BondiR>;
804 0 : using temporary_tags =
805 : tmpl::list<::Tags::SpinWeighted<::Tags::TempScalar<0, ComplexDataVector>,
806 : std::integral_constant<int, 0>>,
807 : ::Tags::SpinWeighted<::Tags::TempScalar<1, ComplexDataVector>,
808 : std::integral_constant<int, 0>>,
809 : ::Tags::SpinWeighted<::Tags::TempScalar<0, ComplexDataVector>,
810 : std::integral_constant<int, 2>>>;
811 :
812 0 : using return_tags =
813 : tmpl::append<tmpl::list<Tags::RegularIntegrand<Tags::BondiH>>,
814 : temporary_tags>;
815 0 : using argument_tags =
816 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
817 : integration_independent_tags>;
818 :
819 : template <typename... Args>
820 0 : static void apply(
821 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*>
822 : regular_integrand_for_h,
823 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
824 : script_aj,
825 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
826 : script_bj,
827 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*>
828 : script_cj,
829 : const Args&... args) {
830 : apply_impl(make_not_null(&get(*regular_integrand_for_h)),
831 : make_not_null(&get(*script_aj)), make_not_null(&get(*script_bj)),
832 : make_not_null(&get(*script_cj)), get(args)...);
833 : }
834 :
835 : private:
836 0 : static void apply_impl(
837 : gsl::not_null<SpinWeighted<ComplexDataVector, 2>*>
838 : regular_integrand_for_h,
839 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> script_aj,
840 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> script_bj,
841 : gsl::not_null<SpinWeighted<ComplexDataVector, 2>*> script_cj,
842 : const SpinWeighted<ComplexDataVector, 2>& dy_dy_j,
843 : const SpinWeighted<ComplexDataVector, 2>& dy_j,
844 : const SpinWeighted<ComplexDataVector, 0>& dy_w,
845 : const SpinWeighted<ComplexDataVector, 0>& exp_2_beta,
846 : const SpinWeighted<ComplexDataVector, 2>& j,
847 : const SpinWeighted<ComplexDataVector, 1>& q,
848 : const SpinWeighted<ComplexDataVector, 1>& u,
849 : const SpinWeighted<ComplexDataVector, 0>& w,
850 : const SpinWeighted<ComplexDataVector, 1>& eth_beta,
851 : const SpinWeighted<ComplexDataVector, 2>& eth_eth_beta,
852 : const SpinWeighted<ComplexDataVector, 0>& eth_ethbar_beta,
853 : const SpinWeighted<ComplexDataVector, 2>& eth_ethbar_j,
854 : const SpinWeighted<ComplexDataVector, 0>& eth_ethbar_j_jbar,
855 : const SpinWeighted<ComplexDataVector, 1>& eth_j_jbar,
856 : const SpinWeighted<ComplexDataVector, 2>& eth_q,
857 : const SpinWeighted<ComplexDataVector, 2>& eth_u,
858 : const SpinWeighted<ComplexDataVector, 2>& eth_ubar_dy_j,
859 : const SpinWeighted<ComplexDataVector, 1>& ethbar_dy_j,
860 : const SpinWeighted<ComplexDataVector, 0>& ethbar_ethbar_j,
861 : const SpinWeighted<ComplexDataVector, 1>& ethbar_j,
862 : const SpinWeighted<ComplexDataVector, -1>& ethbar_jbar_dy_j,
863 : const SpinWeighted<ComplexDataVector, -2>& ethbar_jbar_q_minus_2_eth_beta,
864 : const SpinWeighted<ComplexDataVector, 0>& ethbar_q,
865 : const SpinWeighted<ComplexDataVector, 0>& ethbar_u,
866 : const SpinWeighted<ComplexDataVector, 0>& du_r_divided_by_r,
867 : const SpinWeighted<ComplexDataVector, 1>& eth_r_divided_by_r,
868 : const SpinWeighted<ComplexDataVector, 0>& k,
869 : const SpinWeighted<ComplexDataVector, 0>& one_minus_y,
870 : const SpinWeighted<ComplexDataVector, 0>& r);
871 : };
872 :
873 : /*!
874 : * \brief Computes the linear factor which multiplies \f$H\f$ in the
875 : * equation which determines the radial (y) dependence of the Bondi quantity
876 : * \f$H\f$.
877 : *
878 : * \details The quantity \f$H \equiv \partial_u J\f$ (evaluated at constant y)
879 : * is defined via the Bondi form of the metric:
880 : * \f[ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
881 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
882 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
883 : * angular dyad \f$q^A\f$:
884 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A \bar{q}^B.\f]
885 : * See \cite Bishop1997ik \cite Handmer2014qha for full details.
886 : *
887 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
888 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
889 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
890 : * the worldtube. The equation which determines \f$H\f$ on a surface of constant
891 : * \f$u\f$ given \f$J\f$,\f$\beta\f$, \f$Q\f$, \f$U\f$, and \f$W\f$ on the same
892 : * surface is written as
893 : * \f[(1 - y) \partial_y H + H + (1 - y) J (\mathcal{D}_J
894 : * H + \bar{\mathcal{D}}_J \bar{H}) = A_J + (1 - y) B_J.\f]
895 : * The quantity \f$1 +(1 - y) J \mathcal{D}_J\f$ is the linear factor
896 : * for the non-conjugated \f$H\f$, and is computed from the equation:
897 : * \f[\mathcal{D}_J = \frac{1}{4}(-2 \partial_y \bar{J} + \frac{\bar{J}
898 : * \partial_y (J \bar{J})}{K^2})\f]
899 : */
900 : template <>
901 1 : struct ComputeBondiIntegrand<Tags::LinearFactor<Tags::BondiH>> {
902 : public:
903 0 : using pre_swsh_derivative_tags =
904 : tmpl::list<Tags::Dy<Tags::BondiJ>, Tags::BondiJ>;
905 0 : using swsh_derivative_tags = tmpl::list<>;
906 0 : using integration_independent_tags = tmpl::list<Tags::OneMinusY>;
907 0 : using temporary_tags =
908 : tmpl::list<::Tags::SpinWeighted<::Tags::TempScalar<0, ComplexDataVector>,
909 : std::integral_constant<int, 2>>>;
910 :
911 0 : using return_tags = tmpl::append<tmpl::list<Tags::LinearFactor<Tags::BondiH>>,
912 : temporary_tags>;
913 0 : using argument_tags =
914 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
915 : integration_independent_tags>;
916 :
917 : template <typename... Args>
918 0 : static void apply(
919 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
920 : linear_factor_for_h,
921 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*>
922 : script_djbar,
923 : const Args&... args) {
924 : apply_impl(make_not_null(&get(*linear_factor_for_h)),
925 : make_not_null(&get(*script_djbar)), get(args)...);
926 : }
927 :
928 : private:
929 0 : static void apply_impl(
930 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> linear_factor_for_h,
931 : gsl::not_null<SpinWeighted<ComplexDataVector, 2>*> script_djbar,
932 : const SpinWeighted<ComplexDataVector, 2>& dy_j,
933 : const SpinWeighted<ComplexDataVector, 2>& j,
934 : const SpinWeighted<ComplexDataVector, 0>& one_minus_y);
935 : };
936 :
937 : /*!
938 : * \brief Computes the linear factor which multiplies \f$\bar{H}\f$ in the
939 : * equation which determines the radial (y) dependence of the Bondi quantity
940 : * \f$H\f$.
941 : *
942 : * \details The quantity \f$H \equiv \partial_u J\f$ (evaluated at constant y)
943 : * is defined via the Bondi form of the metric:
944 : * \f[ds^2 = - \left(e^{2 \beta} (1 + r W) - r^2 h_{AB} U^A U^B\right) du^2 - 2
945 : * e^{2 \beta} du dr - 2 r^2 h_{AB} U^B du dx^A + r^2 h_{A B} dx^A dx^B. \f]
946 : * Additional quantities \f$J\f$ and \f$K\f$ are defined using a spherical
947 : * angular dyad \f$q^A\f$:
948 : * \f[ J \equiv h_{A B} q^A q^B, K \equiv h_{A B} q^A \bar{q}^B.\f]
949 : * See \cite Bishop1997ik \cite Handmer2014qha for full details.
950 : *
951 : * We write the equations of motion in the compactified coordinate \f$ y \equiv
952 : * 1 - 2 R/ r\f$, where \f$r(u, \theta, \phi)\f$ is the Bondi radius of the
953 : * \f$y=\f$ constant surface and \f$R(u,\theta,\phi)\f$ is the Bondi radius of
954 : * the worldtube. The equation which determines \f$H\f$ on a surface of constant
955 : * \f$u\f$ given \f$J\f$,\f$\beta\f$, \f$Q\f$, \f$U\f$, and \f$W\f$ on the same
956 : * surface is written as
957 : * \f[(1 - y) \partial_y H + H + (1 - y) J (\mathcal{D}_J H +
958 : * \bar{\mathcal{D}}_J \bar{H}) = A_J + (1 - y) B_J.\f]
959 : * The quantity \f$ (1 - y) J \bar{\mathcal{D}}_J\f$ is the linear factor
960 : * for the non-conjugated \f$H\f$, and is computed from the equation:
961 : * \f[\mathcal{D}_J = \frac{1}{4}(-2 \partial_y \bar{J} + \frac{\bar{J}
962 : * \partial_y (J \bar{J})}{K^2})\f]
963 : */
964 : template <>
965 1 : struct ComputeBondiIntegrand<Tags::LinearFactorForConjugate<Tags::BondiH>> {
966 : public:
967 0 : using pre_swsh_derivative_tags =
968 : tmpl::list<Tags::Dy<Tags::BondiJ>, Tags::BondiJ>;
969 0 : using swsh_derivative_tags = tmpl::list<>;
970 0 : using integration_independent_tags = tmpl::list<Tags::OneMinusY>;
971 0 : using temporary_tags =
972 : tmpl::list<::Tags::SpinWeighted<::Tags::TempScalar<0, ComplexDataVector>,
973 : std::integral_constant<int, 2>>>;
974 :
975 0 : using return_tags =
976 : tmpl::append<tmpl::list<Tags::LinearFactorForConjugate<Tags::BondiH>>,
977 : temporary_tags>;
978 0 : using argument_tags =
979 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
980 : integration_independent_tags>;
981 :
982 : template <typename... Args>
983 0 : static void apply(
984 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 4>>*>
985 : linear_factor_for_conjugate_h,
986 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*>
987 : script_djbar,
988 : const Args&... args) {
989 : apply_impl(make_not_null(&get(*linear_factor_for_conjugate_h)),
990 : make_not_null(&get(*script_djbar)), get(args)...);
991 : }
992 :
993 : private:
994 0 : static void apply_impl(
995 : gsl::not_null<SpinWeighted<ComplexDataVector, 4>*>
996 : linear_factor_for_conjugate_h,
997 : gsl::not_null<SpinWeighted<ComplexDataVector, 2>*> script_djbar,
998 : const SpinWeighted<ComplexDataVector, 2>& dy_j,
999 : const SpinWeighted<ComplexDataVector, 2>& j,
1000 : const SpinWeighted<ComplexDataVector, 0>& one_minus_y);
1001 : };
1002 :
1003 : /*!
1004 : *\brief Computes the pole part of the integrand (right-hand side) of the
1005 : * equation which determines the radial (y) dependence of the scalar quantity
1006 : * \f$\Pi\f$.
1007 : *
1008 : * \details The evolution equation for \f$\Pi\f$ is written as
1009 : * \f[(1 - y) \partial_y \Pi + \Pi = A_\Pi + (1 - y) B_\Pi.\f]
1010 : * We refer to \f$A_\Pi\f$ as the "pole part" of the integrand and \f$B_\Pi\f$
1011 : * as the "regular part". The pole part is computed by this function, and has
1012 : * the expression
1013 : * \f[A_\Pi = - \Re \left(U \bar{\eth}\psi\right).\f]
1014 : */
1015 : template <>
1016 1 : struct ComputeBondiIntegrand<Tags::PoleOfIntegrand<Tags::KleinGordonPi>> {
1017 : public:
1018 0 : using pre_swsh_derivative_tags = tmpl::list<>;
1019 0 : using swsh_derivative_tags =
1020 : tmpl::list<Spectral::Swsh::Tags::Derivative<Tags::KleinGordonPsi,
1021 : Spectral::Swsh::Tags::Eth>>;
1022 0 : using integration_independent_tags = tmpl::list<Tags::BondiU>;
1023 :
1024 0 : using return_tags = tmpl::list<Tags::PoleOfIntegrand<Tags::KleinGordonPi>>;
1025 0 : using argument_tags =
1026 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
1027 : integration_independent_tags>;
1028 :
1029 : template <typename... Args>
1030 0 : static void apply(
1031 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
1032 : pole_of_integrand_for_kg_pi,
1033 : const Args&... args) {
1034 : apply_impl(make_not_null(&get(*pole_of_integrand_for_kg_pi)), get(args)...);
1035 : }
1036 :
1037 : private:
1038 0 : static void apply_impl(gsl::not_null<SpinWeighted<ComplexDataVector, 0>*>
1039 : pole_of_integrand_for_kg_pi,
1040 : const SpinWeighted<ComplexDataVector, 1>& eth_kg_psi,
1041 : const SpinWeighted<ComplexDataVector, 1>& bondi_u);
1042 : };
1043 :
1044 : /*!
1045 : * \brief Computes the regular part of the integrand (right-hand side) of the
1046 : * equation which determines the radial (y) dependence of the scalar quantity
1047 : * \f$\Pi\f$.
1048 : *
1049 : * \details The evolution equation for \f$\Pi\f$ is written as
1050 : * \f[(1 - y) \partial_y \Pi + \Pi = A_\Pi + (1 - y) B_\Pi.\f]
1051 : * We refer to \f$A_\Pi\f$ as the "pole part" of the integrand and \f$B_\Pi\f$
1052 : * as the "regular part". The regular part is computed by this function, and has
1053 : * the expression:
1054 : * \f[ B_\Pi = \frac{1}{4R}e^{2\beta}\left(N_{\psi 1}-N_{\psi 2} +N_{\psi
1055 : * 3}\right) -\frac{R}{2}\frac{N_{\psi 4}}{(1-y)^2}
1056 : * +\tau+\frac{\partial_{u}R}{R}(1-y)\partial_y^2\psi, \f]
1057 : * where
1058 : * \f{align*}{
1059 : * & N_{\psi 1}= K(2\Re \eth\beta\bar{\eth}\psi + \eth\bar{\eth}\psi) \\
1060 : * & N_{\psi 2}=\Re \bar{J}\eth\eth\psi + 2\Re \bar{\eth}\beta \bar{\eth}\psi
1061 : * J + \Re \bar{\eth}J\bar{\eth}\psi \\
1062 : * & N_{\psi 3}=\Re \eth K\bar{\eth}\psi \\
1063 : * & N_{\psi 4}=2\Re (\bar{\eth}\psi ) \partial_rU + 2\Re \eth
1064 : * \bar{U}\partial_r\psi + 4\Re \bar{U}\eth\partial_r\psi \\
1065 : * & \tau=\frac{1}{2}(1-y)\partial_y W\partial_y\psi +
1066 : * \frac{(1-y)^2}{4R}\partial_y^2\psi +
1067 : * \frac{1}{2}(1-y)W\partial_y^2\psi + \frac{1}{2}W\partial_y\psi
1068 : * \f}
1069 : */
1070 : template <>
1071 1 : struct ComputeBondiIntegrand<Tags::RegularIntegrand<Tags::KleinGordonPi>> {
1072 : public:
1073 0 : using pre_swsh_derivative_tags =
1074 : tmpl::list<Tags::Dy<Tags::Dy<Tags::KleinGordonPsi>>,
1075 : Tags::Dy<Tags::KleinGordonPsi>, Tags::Dy<Tags::BondiU>,
1076 : Tags::Dy<Tags::BondiW>>;
1077 0 : using swsh_derivative_tags =
1078 : tmpl::list<Spectral::Swsh::Tags::Derivative<
1079 : Tags::Dy<Tags::KleinGordonPsi>, Spectral::Swsh::Tags::Eth>,
1080 : Spectral::Swsh::Tags::Derivative<Tags::KleinGordonPsi,
1081 : Spectral::Swsh::Tags::EthEth>,
1082 : Spectral::Swsh::Tags::Derivative<Tags::KleinGordonPsi,
1083 : Spectral::Swsh::Tags::Eth>,
1084 : Spectral::Swsh::Tags::Derivative<Tags::BondiJ,
1085 : Spectral::Swsh::Tags::Ethbar>,
1086 : Spectral::Swsh::Tags::Derivative<Tags::BondiU,
1087 : Spectral::Swsh::Tags::Ethbar>,
1088 : Spectral::Swsh::Tags::Derivative<Tags::BondiBeta,
1089 : Spectral::Swsh::Tags::Eth>,
1090 : Spectral::Swsh::Tags::Derivative<
1091 : ::Tags::Multiplies<Tags::BondiJ, Tags::BondiJbar>,
1092 : Spectral::Swsh::Tags::Eth>,
1093 : Spectral::Swsh::Tags::Derivative<
1094 : Tags::KleinGordonPsi, Spectral::Swsh::Tags::EthEthbar>>;
1095 0 : using integration_independent_tags =
1096 : tmpl::list<Tags::BondiJ, Tags::Exp2Beta, Tags::DuRDividedByR,
1097 : Tags::OneMinusY, Tags::EthRDividedByR, Tags::BondiR,
1098 : Tags::BondiK, Tags::BondiU, Tags::BondiW>;
1099 :
1100 0 : using return_tags = tmpl::list<Tags::RegularIntegrand<Tags::KleinGordonPi>>;
1101 0 : using argument_tags =
1102 : tmpl::append<pre_swsh_derivative_tags, swsh_derivative_tags,
1103 : integration_independent_tags>;
1104 :
1105 : template <typename... Args>
1106 0 : static void apply(
1107 : const gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*>
1108 : regular_integrand_for_kg_pi,
1109 : const Args&... args) {
1110 : apply_impl(make_not_null(&get(*regular_integrand_for_kg_pi)), get(args)...);
1111 : }
1112 :
1113 : private:
1114 0 : static void apply_impl(
1115 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*>
1116 : regular_integrand_for_kg_pi,
1117 : // pre_swsh_derivative_tags
1118 : const SpinWeighted<ComplexDataVector, 0>& dy_dy_kg_psi,
1119 : const SpinWeighted<ComplexDataVector, 0>& dy_kg_psi,
1120 : const SpinWeighted<ComplexDataVector, 1>& dy_bondi_u,
1121 : const SpinWeighted<ComplexDataVector, 0>& dy_w,
1122 : // swsh_derivative_tags
1123 : const SpinWeighted<ComplexDataVector, 1>& eth_dy_kg_psi,
1124 : const SpinWeighted<ComplexDataVector, 2>& eth_eth_kg_psi,
1125 : const SpinWeighted<ComplexDataVector, 1>& eth_kg_psi,
1126 : const SpinWeighted<ComplexDataVector, 1>& ethbar_j,
1127 : const SpinWeighted<ComplexDataVector, 0>& ethbar_u,
1128 : const SpinWeighted<ComplexDataVector, 1>& eth_beta,
1129 : const SpinWeighted<ComplexDataVector, 1>& eth_j_jbar,
1130 : const SpinWeighted<ComplexDataVector, 0>& eth_ethbar_kg_psi,
1131 : // integration_independent_tags
1132 : const SpinWeighted<ComplexDataVector, 2>& j,
1133 : const SpinWeighted<ComplexDataVector, 0>& exp2beta,
1134 : const SpinWeighted<ComplexDataVector, 0>& du_r_divided_by_r,
1135 : const SpinWeighted<ComplexDataVector, 0>& one_minus_y,
1136 : const SpinWeighted<ComplexDataVector, 1>& eth_r_divided_by_r,
1137 : const SpinWeighted<ComplexDataVector, 0>& bondi_r,
1138 : const SpinWeighted<ComplexDataVector, 0>& bondi_k,
1139 : const SpinWeighted<ComplexDataVector, 1>& bondi_u,
1140 : const SpinWeighted<ComplexDataVector, 0>& bondi_w);
1141 : };
1142 : } // namespace Cce
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