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 : #include <memory>
8 :
9 : #include "DataStructures/SpinWeighted.hpp"
10 : #include "DataStructures/Tensor/Tensor.hpp"
11 : #include "Evolution/Systems/Cce/AnalyticSolutions/WorldtubeData.hpp"
12 : #include "Evolution/Systems/Cce/Tags.hpp"
13 : #include "Evolution/Systems/GeneralizedHarmonic/Tags.hpp"
14 : #include "Options/String.hpp"
15 : #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
16 : #include "Utilities/Gsl.hpp"
17 : #include "Utilities/Literals.hpp"
18 : #include "Utilities/Serialization/CharmPupable.hpp"
19 : #include "Utilities/TMPL.hpp"
20 :
21 : /// \cond
22 : class DataVector;
23 : /// \endcond
24 :
25 1 : namespace Cce::Solutions {
26 :
27 : /*!
28 : * \brief Analytic solution representing a coordinate oscillation about a
29 : * stationary Schwarzschild black hole.
30 : *
31 : * \details As the oscillation in the metric data at the worldtube is a pure
32 : * coordinate effect, the system evolved using this worldtube data should
33 : * produce zero news. The solution is a coordinate transform applied to the
34 : * Schwarzschild solution in Kerr-Schild coordinates.
35 : */
36 1 : struct BouncingBlackHole : public WorldtubeData {
37 0 : struct Amplitude {
38 0 : using type = double;
39 0 : static constexpr Options::String help{
40 : "The coordinate distance of the gauge oscillation"};
41 0 : static type lower_bound() { return 0.0; }
42 0 : static type suggested_value() { return 2.0; }
43 : };
44 0 : struct ExtractionRadius {
45 0 : using type = double;
46 0 : static constexpr Options::String help{
47 : "The extraction radius of the spherical solution"};
48 0 : static type lower_bound() { return 0.0; }
49 0 : static type suggested_value() { return 20.0; }
50 : };
51 0 : struct Mass {
52 0 : using type = double;
53 0 : static constexpr Options::String help{
54 : "The mass of the Schwarzschild black hole"};
55 0 : static type lower_bound() { return 0.0; }
56 0 : static type suggested_value() { return 1.0; }
57 : };
58 0 : struct Period {
59 0 : using type = double;
60 0 : static constexpr Options::String help{
61 : "The period of the coordinate oscillation"};
62 0 : static type lower_bound() { return 0.0; }
63 0 : static type suggested_value() { return 40.0; }
64 : };
65 :
66 0 : static constexpr Options::String help{
67 : "Analytic solution in which a static black hole is placed in an "
68 : "oscillating coordinate system"};
69 :
70 0 : using options = tmpl::list<Amplitude, ExtractionRadius, Mass, Period>;
71 :
72 0 : WRAPPED_PUPable_decl_template(BouncingBlackHole); // NOLINT
73 :
74 0 : explicit BouncingBlackHole(CkMigrateMessage* msg) : WorldtubeData(msg) {}
75 :
76 : // clang doesn't manage to use = default correctly in this case
77 : // NOLINTNEXTLINE(modernize-use-equals-default)
78 0 : BouncingBlackHole() {}
79 :
80 0 : BouncingBlackHole(double amplitude, double extraction_radius, double mass,
81 : double period);
82 :
83 0 : std::unique_ptr<WorldtubeData> get_clone() const override;
84 :
85 0 : void pup(PUP::er& p) override;
86 :
87 : protected:
88 : // The bouncing black hole solution is easily computed directly, so requires
89 : // no additional preparation.
90 0 : void prepare_solution(const size_t /*l_max*/,
91 : const double /*time*/) const override{};
92 :
93 0 : using WorldtubeData::variables_impl;
94 :
95 : /*!
96 : * \brief The implementation function that computes the spacetime metric on
97 : * the extraction sphere at collocation points associated with angular
98 : * resolution `l_max`.
99 : *
100 : * \details The spacetime metric \f$g_{a b}\f$ is determined by evaluating the
101 : * Kerr-Schild metric at a set of transformed coordinates \f$t^\prime = t,
102 : * y^\prime = y, z^\prime = z\f$, and
103 : *
104 : * \f{align*}{
105 : * x = x^\prime + A \left(\sin\left(\frac{2 \pi t}{T}\right)\right)^4,
106 : * \f}
107 : *
108 : * where the amplitude \f$A\f$ is set by the option `Amplitude` and the period
109 : * \f$T\f$ is set by the option `Period`. In this notation we take
110 : * the primed coordinates to be the coordinates for which the black hole has
111 : * time-dependent coordinate position.
112 : */
113 1 : void variables_impl(
114 : gsl::not_null<tnsr::aa<DataVector, 3>*> spacetime_metric, size_t l_max,
115 : double time,
116 : tmpl::type_<gr::Tags::SpacetimeMetric<DataVector, 3>> /*meta*/)
117 : const override;
118 :
119 : /*!
120 : * \brief The implementation function that computes the first time derivative
121 : * of the spacetime metric on the extraction sphere.
122 : *
123 : * \details The time derivative of the spacetime metric
124 : * \f$\partial_t g_{a b}\f$ comes entirely from the Jacobian factor:
125 : *
126 : * \f{align*}{
127 : * \partial_t x = \frac{8 \pi A}{T} \cos\left(\frac{2 \pi t}{T}\right)
128 : * \left(\sin\left(\frac{2 \pi t}{T}\right)\right)^3,
129 : * \f}
130 : *
131 : * so the transformed metric derivative is,
132 : *
133 : * \f{align*}{
134 : * \partial_t g_{a^\prime b^\prime} = 2 \partial_{(a^\prime} \partial_t x
135 : * \partial_{b^\prime)} x^a g_{x a}.
136 : * \f}
137 : *
138 : * In this notation we take the primed coordinates to be the coordinates for
139 : * which the black hole has time-dependent coordinate position.
140 : */
141 1 : void variables_impl(
142 : gsl::not_null<tnsr::aa<DataVector, 3>*> dt_spacetime_metric, size_t l_max,
143 : double time,
144 : tmpl::type_<
145 : ::Tags::dt<gr::Tags::SpacetimeMetric<DataVector, 3>>> /*meta*/)
146 : const override;
147 :
148 : /*!
149 : * \brief The implementation function that computes the first spatial
150 : * derivative of the spacetime metric on the extraction sphere.
151 : *
152 : * \details The calculation proceeds by standard coordinate transform
153 : * techniques for the transformation given by \f$t^\prime = t,
154 : * y^\prime = y, z^\prime = z\f$, and
155 : *
156 : * \f{align*}{
157 : * x = x^\prime + A \left(\sin\left(\frac{2 \pi t}{T}\right)\right)^4,
158 : * \f}
159 : *
160 : * The general coordinate transformation formula that gives the metric
161 : * is then
162 : * \f{align*}{
163 : * \partial_a g_{b c} =
164 : * \partial_a \partial_b x^{\prime a^\prime} \partial_c x^{\prime b^\prime}
165 : * g_{a^\prime b^\prime}
166 : * + \partial_b x^{\prime a^\prime} \partial_a \partial_c x^{\prime b^\prime}
167 : * g_{a^\prime b^\prime}
168 : * + \partial_a x^{\prime a^\prime} \partial_b x^{\prime b^\prime}
169 : * \partial_c x^{\prime c^\prime} \partial_a g_{b c}
170 : * \f}
171 : */
172 1 : void variables_impl(
173 : gsl::not_null<tnsr::iaa<DataVector, 3>*> d_spacetime_metric, size_t l_max,
174 : double time,
175 : tmpl::type_<gh::Tags::Phi<DataVector, 3>> /*meta*/) const override;
176 :
177 : /// The News in the bouncing black hole solution vanishes, as the oscillation
178 : /// comes entirely from a coordinate transform.
179 1 : void variables_impl(
180 : gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, -2>>*> news,
181 : size_t output_l_max, double time,
182 : tmpl::type_<Tags::News> /*meta*/) const override;
183 :
184 0 : double amplitude_ = std::numeric_limits<double>::signaling_NaN();
185 0 : double mass_ = std::numeric_limits<double>::signaling_NaN();
186 0 : double frequency_ = std::numeric_limits<double>::signaling_NaN();
187 : };
188 : } // namespace Cce::Solutions
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