Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <complex>
7 : #include <cstddef>
8 : #include <limits>
9 : #include <memory>
10 : #include <vector>
11 :
12 : #include "DataStructures/SpinWeighted.hpp"
13 : #include "Evolution/Systems/Cce/AnalyticSolutions/LinearizedBondiSachsInitializeJ.hpp"
14 : #include "Evolution/Systems/Cce/AnalyticSolutions/SphericalMetricData.hpp"
15 : #include "Evolution/Systems/Cce/AnalyticSolutions/WorldtubeData.hpp"
16 : #include "Evolution/Systems/Cce/Initialize/InitializeJ.hpp"
17 : #include "Evolution/Systems/Cce/Tags.hpp"
18 : #include "Options/StdComplex.hpp"
19 : #include "Options/String.hpp"
20 : #include "Utilities/Gsl.hpp"
21 : #include "Utilities/Serialization/CharmPupable.hpp"
22 : #include "Utilities/TMPL.hpp"
23 :
24 : /// \cond
25 : class DataVector;
26 : class ComplexDataVector;
27 : /// \endcond
28 :
29 : namespace Cce::Solutions {
30 : namespace LinearizedBondiSachs_detail {
31 :
32 : // combine the (2,2) and (3,3) modes to collocation values for
33 : // `bondi_quantity`
34 : template <int Spin, typename FactorType>
35 : void assign_components_from_l_factors(
36 : gsl::not_null<SpinWeighted<ComplexDataVector, Spin>*> bondi_quantity,
37 : const FactorType& l_2_factor, const FactorType& l_3_factor, size_t l_max,
38 : double frequency, double time);
39 :
40 : // combine the (2,2) and (3,3) modes to time derivative collocation values for
41 : // `bondi_quantity`
42 : template <int Spin>
43 : void assign_du_components_from_l_factors(
44 : gsl::not_null<SpinWeighted<ComplexDataVector, Spin>*> du_bondi_quantity,
45 : const std::complex<double>& l_2_factor,
46 : const std::complex<double>& l_3_factor, size_t l_max, double frequency,
47 : double time);
48 : } // namespace LinearizedBondiSachs_detail
49 :
50 : /*!
51 : * \brief Computes the analytic data for a Linearized solution to the
52 : * Bondi-Sachs equations described in \cite Barkett2019uae.
53 : *
54 : * \details The solution represented by this function is generated with only
55 : * \f$(2,\pm2)\f$ and \f$(3,\pm3)\f$ modes, and is constructed according to the
56 : * linearized solution documented in Section VI of \cite Barkett2019uae. For
57 : * this solution, we impose additional restrictions that the linearized solution
58 : * be asymptotically flat so that it is compatible with the gauge
59 : * transformations performed in the SpECTRE regularity-preserving CCE. Using the
60 : * notation of \cite Barkett2019uae, we set:
61 : *
62 : * \f{align*}{
63 : * B_2 &= B_3 = 0\\
64 : * C_{2b} &= 3 C_{2a} / \nu^2\\
65 : * C_{3b} &= -3 i C_{3a} / \nu^3
66 : * \f}
67 : *
68 : * where \f$C_{2a}\f$ and \f$C_{3a}\f$ may be specified freely and are taken via
69 : * input option `InitialModes`.
70 : */
71 1 : struct LinearizedBondiSachs : public SphericalMetricData {
72 0 : struct InitialModes {
73 0 : using type = std::array<std::complex<double>, 2>;
74 0 : static constexpr Options::String help{
75 : "The initial modes of the Robinson-Trautman scalar"};
76 : };
77 0 : struct ExtractionRadius {
78 0 : using type = double;
79 0 : static constexpr Options::String help{
80 : "The extraction radius of the spherical solution"};
81 0 : static type lower_bound() { return 0.0; }
82 : };
83 0 : struct Frequency {
84 0 : using type = double;
85 0 : static constexpr Options::String help{
86 : "The frequency of the linearized modes."};
87 0 : static type lower_bound() { return 0.0; }
88 : };
89 :
90 0 : static constexpr Options::String help{
91 : "A linearized Bondi-Sachs analytic solution"};
92 :
93 0 : using options = tmpl::list<InitialModes, ExtractionRadius, Frequency>;
94 :
95 0 : WRAPPED_PUPable_decl_template(LinearizedBondiSachs); // NOLINT
96 :
97 0 : explicit LinearizedBondiSachs(CkMigrateMessage* msg)
98 : : SphericalMetricData(msg) {}
99 :
100 : // clang doesn't manage to use = default correctly in this case
101 : // NOLINTNEXTLINE(hicpp-use-equals-default,modernize-use-equals-default)
102 0 : LinearizedBondiSachs() {}
103 :
104 0 : LinearizedBondiSachs(
105 : const std::array<std::complex<double>, 2>& mode_constants,
106 : double extraction_radius, double frequency);
107 :
108 0 : std::unique_ptr<WorldtubeData> get_clone() const override;
109 :
110 0 : void pup(PUP::er& p) override;
111 :
112 0 : std::unique_ptr<Cce::InitializeJ::InitializeJ<false>> get_initialize_j(
113 : double start_time) const override;
114 :
115 : protected:
116 : /// A no-op as the linearized solution does not have substantial shared
117 : /// computation to prepare before the separate component calculations.
118 1 : void prepare_solution(const size_t /*output_l_max*/,
119 : const double /*time*/) const override {}
120 :
121 : /*!
122 : * \brief Computes the linearized solution for \f$J\f$.
123 : *
124 : * \details The linearized solution for \f$J\f$ is given by
125 : * \cite Barkett2019uae,
126 : *
127 : * \f[
128 : * J = \sqrt{12} ({}_2 Y_{2\,2} + {}_2 Y_{2\, -2})
129 : * \mathrm{Re}(J_2(r) e^{i \nu u})
130 : * + \sqrt{60} ({}_2 Y_{3\,3} - {}_2 Y_{3\, -3})
131 : * \mathrm{Re}(J_3(r) e^{i \nu u}),
132 : * \f]
133 : *
134 : * where
135 : *
136 : * \f{align*}{
137 : * J_2(r) &= \frac{C_{2a}}{4 r} - \frac{C_{2b}}{12 r^3}, \\
138 : * J_3(r) &= \frac{C_{3a}}{10 r} - \frac{i \nu C_{3 b}}{6 r^3}
139 : * - \frac{C_{3 b}}{4 r^4}.
140 : * \f}
141 : */
142 1 : void linearized_bondi_j(
143 : gsl::not_null<SpinWeighted<ComplexDataVector, 2>*> bondi_j, size_t l_max,
144 : double time) const;
145 :
146 : /*!
147 : * \brief Compute the linearized solution for \f$U\f$
148 : *
149 : * \details The linearized solution for \f$U\f$ is given by
150 : * \cite Barkett2019uae,
151 : *
152 : * \f[
153 : * U = \sqrt{3} ({}_1 Y_{2\,2} + {}_1 Y_{2\, -2})
154 : * \mathrm{Re}(U_2(r) e^{i \nu u})
155 : * + \sqrt{6} ({}_1 Y_{3\,3} - {}_1 Y_{3\, -3})
156 : * \mathrm{Re}(U_3(r) e^{i \nu u}),
157 : * \f]
158 : *
159 : * where
160 : *
161 : * \f{align*}{
162 : * U_2(r) &= \frac{C_{2a}}{2 r^2} + \frac{i \nu C_{2 b}}{3 r^3}
163 : * + \frac{C_{2b}}{4 r^4} \\
164 : * U_3(r) &= \frac{C_{3a}}{2 r^2} - \frac{2 \nu^2 C_{3b}}{3 r^3}
165 : * + \frac{5 i \nu C_{3b}}{4 r^4} + \frac{C_{3 b}}{r^5}
166 : * \f}
167 : */
168 1 : void linearized_bondi_u(
169 : gsl::not_null<SpinWeighted<ComplexDataVector, 1>*> bondi_u, size_t l_max,
170 : double time) const;
171 :
172 : /*!
173 : * \brief Computes the linearized solution for \f$W\f$.
174 : *
175 : * \details The linearized solution for \f$W\f$ is given by
176 : * \cite Barkett2019uae,
177 : *
178 : * \f[
179 : * W = \frac{1}{\sqrt{2}} ({}_0 Y_{2\,2} + {}_0 Y_{2\, -2})
180 : * \mathrm{Re}(W_2(r) e^{i \nu u})
181 : * + \frac{1}{\sqrt{2}} ({}_0 Y_{3\,3} - {}_0 Y_{3\, -3})
182 : * \mathrm{Re}(W_3(r) e^{i \nu u}),
183 : * \f]
184 : *
185 : * where
186 : *
187 : * \f{align*}{
188 : * W_2(r) &= - \frac{\nu^2 C_{2b}}{r^2} + \frac{i \nu C_{2 b}}{r^3}
189 : * + \frac{C_{2b}}{2 r^4}, \\
190 : * W_3(r) &= -\frac{2 i \nu^3 C_{3b}}{r^2} - \frac{4 i \nu^2 C_{3b}}{r^3}
191 : * + \frac{5 \nu C_{3b}}{2 r^4} + \frac{3 C_{3b}}{r^5}.
192 : * \f}
193 : */
194 1 : void linearized_bondi_w(
195 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> bondi_w, size_t l_max,
196 : double time) const;
197 :
198 : /*!
199 : * \brief Computes the linearized solution for \f$\partial_r J\f$.
200 : *
201 : * \details The linearized solution for \f$\partial_r J\f$ is given by
202 : * \cite Barkett2019uae,
203 : *
204 : * \f[
205 : * \partial_r J = \sqrt{12} ({}_2 Y_{2\,2} + {}_2 Y_{2\, -2})
206 : * \mathrm{Re}(\partial_r J_2(r) e^{i \nu u})
207 : * + \sqrt{60} ({}_2 Y_{3\,3} - {}_2 Y_{3\, -3})
208 : * \mathrm{Re}(\partial_r J_3(r) e^{i \nu u}),
209 : * \f]
210 : *
211 : * where
212 : *
213 : * \f{align*}{
214 : * \partial_r J_2(r) &= - \frac{C_{2a}}{4 r^2} + \frac{C_{2b}}{4 r^4}, \\
215 : * \partial_r J_3(r) &= -\frac{C_{3a}}{10 r^2} + \frac{i \nu C_{3 b}}{2 r^4}
216 : * + \frac{C_{3 b}}{r^5}.
217 : * \f}
218 : */
219 1 : void linearized_dr_bondi_j(
220 : gsl::not_null<SpinWeighted<ComplexDataVector, 2>*> dr_bondi_j,
221 : size_t l_max, double time) const;
222 :
223 : /*!
224 : * \brief Compute the linearized solution for \f$\partial_r U\f$
225 : *
226 : * \details The linearized solution for \f$\partial_r U\f$ is given by
227 : * \cite Barkett2019uae,
228 : *
229 : * \f[
230 : * \partial_r U = \sqrt{3} ({}_1 Y_{2\,2} + {}_1 Y_{2\, -2})
231 : * \mathrm{Re}(\partial_r U_2(r) e^{i \nu u})
232 : * + \sqrt{6} ({}_1 Y_{3\,3} - {}_1 Y_{3\, -3})
233 : * \mathrm{Re}(\partial_r U_3(r) e^{i \nu u}),
234 : * \f]
235 : *
236 : * where
237 : *
238 : * \f{align*}{
239 : * \partial_r U_2(r) &= -\frac{C_{2a}}{r^3} - \frac{i \nu C_{2 b}}{r^4}
240 : * - \frac{C_{2b}}{r^5} \\
241 : * \partial_r U_3(r) &= -\frac{C_{3a}}{r^3} + \frac{2 \nu^2 C_{3b}}{r^4}
242 : * - \frac{5 i \nu C_{3b}}{r^5} - \frac{5 C_{3 b}}{r^6}
243 : * \f}
244 : */
245 1 : void linearized_dr_bondi_u(
246 : gsl::not_null<SpinWeighted<ComplexDataVector, 1>*> dr_bondi_u,
247 : size_t l_max, double time) const;
248 :
249 : /*!
250 : * \brief Computes the linearized solution for \f$\partial_r W\f$.
251 : *
252 : * \details The linearized solution for \f$W\f$ is given by
253 : * \cite Barkett2019uae,
254 : *
255 : * \f[
256 : * \partial_r W = \frac{1}{\sqrt{2}} ({}_0 Y_{2\,2} + {}_0 Y_{2\, -2})
257 : * \mathrm{Re}(\partial_r W_2(r) e^{i \nu u})
258 : * + \frac{1}{\sqrt{2}} ({}_0 Y_{3\,3} - {}_0 Y_{3\, -3})
259 : * \mathrm{Re}(\partial_r W_3(r) e^{i \nu u}),
260 : * \f]
261 : *
262 : * where
263 : *
264 : * \f{align*}{
265 : * \partial_r W_2(r) &= \frac{2 \nu^2 C_{2b}}{r^3}
266 : * - \frac{3 i \nu C_{2 b}}{r^4} - \frac{2 C_{2b}}{r^5}, \\
267 : * \partial_r W_3(r) &= \frac{4 i \nu^3 C_{3b}}{r^3}
268 : * + \frac{12 i \nu^2 C_{3b}}{r^4} - \frac{10 \nu C_{3b}}{r^5}
269 : * - \frac{15 C_{3b}}{r^6}.
270 : * \f}
271 : */
272 1 : void linearized_dr_bondi_w(
273 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> dr_bondi_w,
274 : size_t l_max, double time) const;
275 :
276 : /*!
277 : * \brief Computes the linearized solution for \f$\partial_u J\f$.
278 : *
279 : * \details The linearized solution for \f$\partial_u J\f$ is given by
280 : * \cite Barkett2019uae,
281 : *
282 : * \f[
283 : * \partial_u J = \sqrt{12} ({}_2 Y_{2\,2} + {}_2 Y_{2\, -2})
284 : * \mathrm{Re}(i \nu J_2(r) e^{i \nu u})
285 : * + \sqrt{60} ({}_2 Y_{3\,3} - {}_2 Y_{3\, -3})
286 : * \mathrm{Re}(i \nu J_3(r) e^{i \nu u}),
287 : * \f]
288 : *
289 : * where
290 : *
291 : * \f{align*}{
292 : * J_2(r) &= \frac{C_{2a}}{4 r} - \frac{C_{2b}}{12 r^3}, \\
293 : * J_3(r) &= \frac{C_{3a}}{10 r} - \frac{i \nu C_{3 b}}{6 r^3}
294 : * - \frac{C_{3 b}}{4 r^4}.
295 : * \f}
296 : */
297 1 : void linearized_du_bondi_j(
298 : gsl::not_null<SpinWeighted<ComplexDataVector, 2>*> du_bondi_j,
299 : size_t l_max, double time) const;
300 :
301 : /*!
302 : * \brief Compute the linearized solution for \f$\partial_u U\f$
303 : *
304 : * \details The linearized solution for \f$U\f$ is given by
305 : * \cite Barkett2019uae,
306 : *
307 : * \f[
308 : * \partial_u U = \sqrt{3} ({}_2 Y_{2\,2} + {}_2 Y_{2\, -2})
309 : * \mathrm{Re}(i \nu U_2(r) e^{i \nu u})
310 : * + \sqrt{6} ({}_2 Y_{3\,3} - {}_2 Y_{3\, -3})
311 : * \mathrm{Re}(i \nu U_3(r) e^{i \nu u}),
312 : * \f]
313 : *
314 : * where
315 : *
316 : * \f{align*}{
317 : * U_2(r) &= \frac{C_{2a}}{2 r^2} + \frac{i \nu C_{2 b}}{3 r^3}
318 : * + \frac{C_{2b}}{4 r^4} \\
319 : * U_3(r) &= \frac{C_{3a}}{2 r^2} - \frac{2 \nu^2 C_{3b}}{3 r^3}
320 : * + \frac{5 i \nu C_{3b}}{4 r^4} + \frac{C_{3 b}}{r^5}
321 : * \f}
322 : */
323 1 : void linearized_du_bondi_u(
324 : gsl::not_null<SpinWeighted<ComplexDataVector, 1>*> du_bondi_u,
325 : size_t l_max, double time) const;
326 :
327 : /*!
328 : * \brief Computes the linearized solution for \f$\partial_u W\f$.
329 : *
330 : * \details The linearized solution for \f$\partial_u W\f$ is given by
331 : * \cite Barkett2019uae,
332 : *
333 : * \f[
334 : * \partial_u W = \frac{1}{\sqrt{2}} ({}_1 Y_{2\,2} + {}_1 Y_{2\, -2})
335 : * \mathrm{Re}(i \nu W_2(r) e^{i \nu u})
336 : * + \frac{1}{\sqrt{2}} ({}_1 Y_{3\,3} - {}_1 Y_{3\, -3})
337 : * \mathrm{Re}(i \nu W_3(r) e^{i \nu u}),
338 : * \f]
339 : *
340 : * where
341 : *
342 : * \f{align*}{
343 : * W_2(r) &= \frac{\nu^2 C_{2b}}{r^2} + \frac{i \nu C_{2 b}}{r^3}
344 : * + \frac{C_{2b}}{2 r^4}, \\
345 : * W_3(r) &= \frac{2 i \nu^3 C_{3b}}{r^2} - \frac{4 i \nu^2 C_{3b}}{r^3}
346 : * + \frac{5 \nu C_{3b}}{2 r^4} + \frac{3 C_{3b}}{r^5}.
347 : * \f}
348 : */
349 1 : void linearized_du_bondi_w(
350 : gsl::not_null<SpinWeighted<ComplexDataVector, 0>*> du_bondi_w,
351 : size_t l_max, double time) const;
352 :
353 : /*!
354 : * \brief Compute the spherical coordinate metric from the linearized
355 : * Bondi-Sachs system.
356 : *
357 : * \details This function dispatches to the individual computations in this
358 : * class to determine the Bondi-Sachs scalars for the linearized solution.
359 : * Once the scalars are determined, the metric is assembled via (note
360 : * \f$\beta = 0\f$ in this solution)
361 : *
362 : * \f{align*}{
363 : * ds^2 =& - ((1 + r W) - r^2 h_{A B} U^A U^B) (dt - dr)^2
364 : * - 2 (dt - dr) dr \\
365 : * &- 2 r^2 h_{A B} U^B (dt - dr) dx^A + r^2 h_{A B} dx^A dx^B,
366 : * \f}
367 : *
368 : * where indices with capital letters refer to angular coordinates and the
369 : * angular tensors may be written in terms of spin-weighted scalars. Doing so
370 : * gives the metric components,
371 : *
372 : * \f{align*}{
373 : * g_{t t} &= -\left(1 + r W
374 : * - r^2 \Re\left(\bar J U^2 + K U \bar U\right)\right)\\
375 : * g_{t r} &= -1 - g_{t t}\\
376 : * g_{r r} &= 2 + g_{t t}\\
377 : * g_{t \theta} &= r^2 \Re\left(K U + J \bar U\right)\\
378 : * g_{t \phi} &= r^2 \Im\left(K U + J \bar U\right)\\
379 : * g_{r \theta} &= -g_{t \theta}\\
380 : * g_{r \phi} &= -g_{t \phi}\\
381 : * g_{\theta \theta} &= r^2 \Re\left(J + K\right)\\
382 : * g_{\theta \phi} &= r^2 \Im\left(J\right)\\
383 : * g_{\phi \phi} &= r^2 \Re\left(K - J\right),
384 : * \f}
385 : *
386 : * and all other components are zero.
387 : */
388 1 : void spherical_metric(
389 : gsl::not_null<
390 : tnsr::aa<DataVector, 3, ::Frame::Spherical<::Frame::Inertial>>*>
391 : spherical_metric,
392 : size_t l_max, double time) const override;
393 :
394 : /*!
395 : * \brief Compute the radial derivative of the spherical coordinate metric
396 : * from the linearized Bondi-Sachs system.
397 : *
398 : * \details This function dispatches to the individual computations in this
399 : * class to determine the Bondi-Sachs scalars for the linearized solution.
400 : * Once the scalars are determined, the radial derivative of the metric is
401 : * assembled via (note \f$\beta = 0\f$ in this solution)
402 : *
403 : * \f{align*}{
404 : * \partial_r g_{a b} dx^a dx^b =& - (W + r \partial_r W
405 : * - 2 r h_{A B} U^A U^B - r^2 (\partial_r h_{A B}) U^A U^B
406 : * - 2 r^2 h_{A B} U^A \partial_r U^B) (dt - dr)^2 \\
407 : * &- (4 r h_{A B} U^B + 2 r^2 ((\partial_r h_{A B}) U^B
408 : * + h_{AB} \partial_r U^B) ) (dt - dr) dx^A
409 : * + (2 r h_{A B} + r^2 \partial_r h_{A B}) dx^A dx^B,
410 : * \f}
411 : *
412 : * where indices with capital letters refer to angular coordinates and the
413 : * angular tensors may be written in terms of spin-weighted scalars. Doing so
414 : * gives the metric components,
415 : *
416 : * \f{align*}{
417 : * \partial_r g_{t t} &= -\left( W + r \partial_r W
418 : * - 2 r \Re\left(\bar J U^2 + K U \bar U\right)
419 : * - r^2 \partial_r \Re\left(\bar J U^2 + K U \bar U\right)\right) \\
420 : * \partial_r g_{t r} &= -\partial_r g_{t t}\\
421 : * \partial_r g_{t \theta} &= 2 r \Re\left(K U + J \bar U\right)
422 : * + r^2 \partial_r \Re\left(K U + J \bar U\right) \\
423 : * \partial_r g_{t \phi} &= 2r \Im\left(K U + J \bar U\right)
424 : * + r^2 \partial_r \Im\left(K U + J \bar U\right) \\
425 : * \partial_r g_{r r} &= \partial_r g_{t t}\\
426 : * \partial_r g_{r \theta} &= -\partial_r g_{t \theta}\\
427 : * \partial_r g_{r \phi} &= -\partial_r g_{t \phi}\\
428 : * \partial_r g_{\theta \theta} &= 2 r \Re\left(J + K\right)
429 : * + r^2 \Re\left(\partial_r J + \partial_r K\right) \\
430 : * \partial_r g_{\theta \phi} &= 2 r \Im\left(J\right)
431 : * + r^2 \Im\left(\partial_r J\right)\\
432 : * \partial_r g_{\phi \phi} &= 2 r \Re\left(K - J\right)
433 : * + r^2 \Re\left(\partial_r K - \partial_r J\right),
434 : * \f}
435 : *
436 : * and all other components are zero.
437 : */
438 1 : void dr_spherical_metric(
439 : gsl::not_null<
440 : tnsr::aa<DataVector, 3, ::Frame::Spherical<::Frame::Inertial>>*>
441 : dr_spherical_metric,
442 : size_t l_max, double time) const override;
443 :
444 : /*!
445 : * \brief Compute the time derivative of the spherical coordinate metric from
446 : * the linearized Bondi-Sachs system.
447 : *
448 : * \details This function dispatches to the individual computations in this
449 : * class to determine the Bondi-Sachs scalars for the linearized solution.
450 : * Once the scalars are determined, the metric is assembled via (note
451 : * \f$\beta = 0\f$ in this solution, and note that we take coordinate
452 : * \f$t=u\f$ in converting to the Cartesian coordinates)
453 : *
454 : * \f{align*}{
455 : * \partial_t g_{a b} dx^a dx^b =& - (r \partial_u W
456 : * - r^2 \partial_u h_{A B} U^A U^B
457 : * - 2 r^2 h_{A B} U^B \partial_u U^A) (dt - dr)^2 \\
458 : * &- 2 r^2 (\partial_u h_{A B} U^B + h_{A B} \partial_u U^B) (dt - dr) dx^A
459 : * + r^2 \partial_u h_{A B} dx^A dx^B,
460 : * \f}
461 : *
462 : * where indices with capital letters refer to angular coordinates and the
463 : * angular tensors may be written in terms of spin-weighted scalars. Doing so
464 : * gives the metric components,
465 : *
466 : * \f{align*}{
467 : * \partial_t g_{t t} &= -\left(r \partial_u W
468 : * - r^2 \partial_u \Re\left(\bar J U^2 + K U \bar U\right)\right)\\
469 : * \partial_t g_{t r} &= -\partial_t g_{t t}\\
470 : * \partial_t g_{t \theta} &= r^2 \partial_u \Re\left(K U + J \bar U\right)\\
471 : * \partial_t g_{t \phi} &= r^2 \partial_u \Im\left(K U + J \bar U\right)\\
472 : * \partial_t g_{r r} &= \partial_t g_{t t}\\
473 : * \partial_t g_{r \theta} &= -\partial_t g_{t \theta}\\
474 : * \partial_t g_{r \phi} &= -\partial_t g_{t \phi}\\
475 : * \partial_t g_{\theta \theta} &= r^2 \Re\left(\partial_u J
476 : * + \partial_u K\right)\\
477 : * \partial_t g_{\theta \phi} &= r^2 \Im\left(\partial_u J\right)\\
478 : * \partial_t g_{\phi \phi} &= r^2 \Re\left(\partial_u K
479 : * - \partial_u J\right),
480 : * \f}
481 : *
482 : * and all other components are zero.
483 : */
484 1 : void dt_spherical_metric(
485 : gsl::not_null<
486 : tnsr::aa<DataVector, 3, ::Frame::Spherical<::Frame::Inertial>>*>
487 : dt_spherical_metric,
488 : size_t l_max, double time) const override;
489 :
490 0 : using WorldtubeData::variables_impl;
491 :
492 1 : using SphericalMetricData::variables_impl;
493 :
494 : /*!
495 : * \brief Determines the News function from the linearized solution
496 : * parameters.
497 : *
498 : * \details The News is determined from the formula given in
499 : * \cite Barkett2019uae,
500 : *
501 : * \f{align*}{
502 : * N = \frac{1}{2 \sqrt{3}} ({}_{-2} Y_{2\, 2} + {}_{-2} Y_{2\,-2})
503 : * \Re\left(i \nu^3 C_{2 b} e^{i \nu u}\right)
504 : * + \frac{1}{\sqrt{15}} ({}_{-2} Y_{3\, 3} - {}_{-2} Y_{3\, -3})
505 : * \Re\left(- \nu^4 C_{3 b} e^{i \nu u} \right)
506 : * \f}
507 : */
508 1 : void variables_impl(
509 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, -2>>*> news,
510 : size_t l_max, double time,
511 : tmpl::type_<Tags::News> /*meta*/) const override;
512 :
513 0 : std::complex<double> c_2a_ = std::numeric_limits<double>::signaling_NaN();
514 0 : std::complex<double> c_3a_ = std::numeric_limits<double>::signaling_NaN();
515 0 : std::complex<double> c_2b_ = std::numeric_limits<double>::signaling_NaN();
516 0 : std::complex<double> c_3b_ = std::numeric_limits<double>::signaling_NaN();
517 :
518 0 : double frequency_ = 0.0;
519 : };
520 : } // namespace Cce::Solutions
|
