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