Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include "DataStructures/DataVector.hpp"
7 : #include "DataStructures/Tensor/Tensor.hpp"
8 : #include "Utilities/Gsl.hpp"
9 :
10 : namespace Xcts {
11 :
12 : /// @{
13 : /*!
14 : * \brief Surface integrand for the ADM linear momentum calculation.
15 : *
16 : * We define the ADM linear momentum integral as (see Eqs. 19-20 in
17 : * \cite Ossokine2015yla):
18 : *
19 : * \begin{equation}
20 : * P_\text{ADM}^i = \frac{1}{8\pi}
21 : * \oint_{S_\infty} \psi^{10} \Big(
22 : * K^{ij} - K \gamma^{ij}
23 : * \Big) \, dS_j.
24 : * \end{equation}
25 : *
26 : * \note For consistency with `adm_linear_momentum_volume_integrand`, this
27 : * integrand needs to be contracted with the Euclidean face normal and
28 : * integrated with the Euclidean area element.
29 : *
30 : * \param result output pointer
31 : * \param conformal_factor the conformal factor $\psi$
32 : * \param inv_spatial_metric the inverse spatial metric $\gamma^{ij}$
33 : * \param inv_extrinsic_curvature the inverse extrinsic curvature $K^{ij}$
34 : * \param trace_extrinsic_curvature the trace of the extrinsic curvature $K$
35 : */
36 1 : void adm_linear_momentum_surface_integrand(
37 : gsl::not_null<tnsr::II<DataVector, 3>*> result,
38 : const Scalar<DataVector>& conformal_factor,
39 : const tnsr::II<DataVector, 3>& inv_spatial_metric,
40 : const tnsr::II<DataVector, 3>& inv_extrinsic_curvature,
41 : const Scalar<DataVector>& trace_extrinsic_curvature);
42 :
43 : /// Return-by-value overload
44 1 : tnsr::II<DataVector, 3> adm_linear_momentum_surface_integrand(
45 : const Scalar<DataVector>& conformal_factor,
46 : const tnsr::II<DataVector, 3>& inv_spatial_metric,
47 : const tnsr::II<DataVector, 3>& inv_extrinsic_curvature,
48 : const Scalar<DataVector>& trace_extrinsic_curvature);
49 : /// @}
50 :
51 : /// @{
52 : /*!
53 : * \brief Volume integrand for ADM linear momentum calculation defined as (see
54 : * Eq. 20 in \cite Ossokine2015yla):
55 : *
56 : * \begin{equation}
57 : * P_\text{ADM}^i = - \frac{1}{8\pi}
58 : * \int_{V_\infty} \Big(
59 : * \bar\Gamma^i_{jk} P^{jk}
60 : * + \bar\Gamma^j_{jk} P^{jk}
61 : * - 2 \bar\gamma_{jk} P^{jk} \bar\gamma^{il}
62 : * \partial_l(\ln\psi)
63 : * \Big) \, dV,
64 : * \end{equation}
65 : *
66 : * where $1/(8\pi) P^{jk}$ is the result from
67 : * `adm_linear_momentum_surface_integrand`.
68 : *
69 : * \note For consistency with `adm_linear_momentum_surface_integrand`, this
70 : * integrand needs to be integrated with the Euclidean volume element.
71 : *
72 : * \param result output pointer
73 : * \param surface_integrand the quantity $1/(8\pi) P^{ij}$ (result of
74 : * `adm_linear_momentum_surface_integrand`)
75 : * \param conformal_factor the conformal factor $\psi$
76 : * \param deriv_conformal_factor the gradient of the conformal factor
77 : * $\partial_i\psi$
78 : * \param conformal_metric the conformal metric $\bar\gamma_{ij}$
79 : * \param inv_conformal_metric the inverse conformal metric $\bar\gamma^{ij}$
80 : * \param conformal_christoffel_second_kind the conformal christoffel symbol
81 : * $\bar\Gamma^i_{jk}$
82 : * \param conformal_christoffel_contracted the contracted conformal christoffel
83 : * symbol $\bar\Gamma_i$
84 : */
85 1 : void adm_linear_momentum_volume_integrand(
86 : gsl::not_null<tnsr::I<DataVector, 3>*> result,
87 : const tnsr::II<DataVector, 3>& surface_integrand,
88 : const Scalar<DataVector>& conformal_factor,
89 : const tnsr::i<DataVector, 3>& deriv_conformal_factor,
90 : const tnsr::ii<DataVector, 3>& conformal_metric,
91 : const tnsr::II<DataVector, 3>& inv_conformal_metric,
92 : const tnsr::Ijj<DataVector, 3>& conformal_christoffel_second_kind,
93 : const tnsr::i<DataVector, 3>& conformal_christoffel_contracted);
94 :
95 : /// Return-by-value overload
96 1 : tnsr::I<DataVector, 3> adm_linear_momentum_volume_integrand(
97 : const tnsr::II<DataVector, 3>& surface_integrand,
98 : const Scalar<DataVector>& conformal_factor,
99 : const tnsr::i<DataVector, 3>& deriv_conformal_factor,
100 : const tnsr::ii<DataVector, 3>& conformal_metric,
101 : const tnsr::II<DataVector, 3>& inv_conformal_metric,
102 : const tnsr::Ijj<DataVector, 3>& conformal_christoffel_second_kind,
103 : const tnsr::i<DataVector, 3>& conformal_christoffel_contracted);
104 : /// @}
105 :
106 : /// @{
107 : /*!
108 : * \brief Surface integrand for the z-component of the ADM angular momentum.
109 : *
110 : * We define the ADM angular momentum surface integral as (see Eq. 23 in
111 : * \cite Ossokine2015yla):
112 : *
113 : * \begin{equation}
114 : * J_\text{ADM}^z = \frac{1}{8\pi}
115 : * \oint_{S_\infty} \Big(
116 : * x P^{yj} - y P^{xj}
117 : * \Big) \, dS_j,
118 : * \end{equation}
119 : *
120 : * where $1/(8\pi) P^{jk}$ is the result from
121 : * `adm_linear_momentum_surface_integrand`.
122 : *
123 : * \note For consistency with `adm_angular_momentum_z_volume_integrand`, this
124 : * integrand needs to be contracted with the Euclidean face normal and
125 : * integrated with the Euclidean area element.
126 : *
127 : * \param result output pointer
128 : * \param linear_momentum_surface_integrand the quantity $1/(8\pi) P^{ij}$
129 : * (result of `adm_linear_momentum_surface_integrand`)
130 : * \param coords the inertial coordinates $x^i$
131 : */
132 1 : void adm_angular_momentum_z_surface_integrand(
133 : gsl::not_null<tnsr::I<DataVector, 3>*> result,
134 : const tnsr::II<DataVector, 3>& linear_momentum_surface_integrand,
135 : const tnsr::I<DataVector, 3>& coords);
136 :
137 : /// Return-by-value overload
138 1 : tnsr::I<DataVector, 3> adm_angular_momentum_z_surface_integrand(
139 : const tnsr::II<DataVector, 3>& linear_momentum_surface_integrand,
140 : const tnsr::I<DataVector, 3>& coords);
141 : /// @}
142 :
143 : /// @{
144 : /*!
145 : * \brief Volume integrand for the z-component of the ADM angular momentum.
146 : *
147 : * We define the ADM angular momentum volume integral as (see Eq. 23 in
148 : * \cite Ossokine2015yla):
149 : *
150 : * \begin{equation}
151 : * J_\text{ADM}^z = - \frac{1}{8\pi}
152 : * \int_{V_\infty} \Big(
153 : * x G^y - y G^x
154 : * \Big) \, dV,
155 : * \end{equation}
156 : *
157 : * where $-1/(8\pi) G^i$ is the result from
158 : * `adm_linear_momentum_volume_integrand`.
159 : *
160 : * \note For consistency with `adm_angular_momentum_z_surface_integrand`, this
161 : * integrand needs to be integrated with the Euclidean volume element.
162 : *
163 : * \param result output pointer
164 : * \param linear_momentum_volume_integrand the quantity $-1/(8\pi) G^i$ (result
165 : * of `adm_linear_momentum_volume_integrand`)
166 : * \param coords the inertial coordinates $x^i$
167 : */
168 1 : void adm_angular_momentum_z_volume_integrand(
169 : gsl::not_null<Scalar<DataVector>*> result,
170 : const tnsr::I<DataVector, 3>& linear_momentum_volume_integrand,
171 : const tnsr::I<DataVector, 3>& coords);
172 :
173 : /// Return-by-value overload
174 1 : Scalar<DataVector> adm_angular_momentum_z_volume_integrand(
175 : const tnsr::I<DataVector, 3>& linear_momentum_volume_integrand,
176 : const tnsr::I<DataVector, 3>& coords);
177 : /// @}
178 :
179 : } // namespace Xcts
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