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              : 
       8              : #include "DataStructures/Tensor/TypeAliases.hpp"
       9              : #include "Utilities/Gsl.hpp"
      10              : 
      11              : namespace Xcts {
      12              : 
      13              : /// @{
      14              : /*!
      15              :  * \brief Extrinsic curvature computed from the conformal decomposition used in
      16              :  * the XCTS system.
      17              :  *
      18              :  * The extrinsic curvature decomposition is (see Eq. 3.113 in
      19              :  * \cite BaumgarteShapiro):
      20              :  *
      21              :  * \begin{equation}
      22              :  *   K_{ij} = A_{ij} + \frac{1}{3}\gamma_{ij}K
      23              :  *     = \frac{\psi^4}{2\lapse}\left((\bar{L}\beta)_{ij} - \bar{u}_{ij}\right)
      24              :  *       + \frac{\psi^4}{3} \bar{\gamma}_{ij} K
      25              :  * \end{equation}
      26              :  *
      27              :  * \param result output buffer for the extrinsic curvature
      28              :  * \param conformal_factor the conformal factor $\psi$
      29              :  * \param lapse the lapse $\alpha$
      30              :  * \param conformal_metric the conformal metric $\bar{\gamma}_{ij}$
      31              :  * \param longitudinal_shift_minus_dt_conformal_metric the term
      32              :  * $(\bar{L}\beta)^{ij} - \bar{u}^{ij}$. Note that $(\bar{L}\beta)^{ij}$ is the
      33              :  * _conformal_ longitudinal shift, and $(\bar{L}\beta)^{ij}=\psi^4(L\beta)^{ij}$
      34              :  * (Eq. 3.98 in \cite BaumgarteShapiro). See also Xcts::longitudinal_operator.
      35              :  * \param trace_extrinsic_curvature the trace of the extrinsic curvature,
      36              :  * $K=\gamma^{ij}K_{ij}$. Note that it is a conformal invariant, $K=\bar{K}$ (by
      37              :  * choice).
      38              :  */
      39              : template <typename DataType>
      40            1 : void extrinsic_curvature(
      41              :     const gsl::not_null<tnsr::ii<DataType, 3>*> result,
      42              :     const Scalar<DataType>& conformal_factor, const Scalar<DataType>& lapse,
      43              :     const tnsr::ii<DataType, 3>& conformal_metric,
      44              :     const tnsr::II<DataType, 3>& longitudinal_shift_minus_dt_conformal_metric,
      45              :     const Scalar<DataType>& trace_extrinsic_curvature);
      46              : 
      47              : /// Return-by-value overload
      48              : template <typename DataType>
      49            1 : tnsr::ii<DataType, 3> extrinsic_curvature(
      50              :     const Scalar<DataType>& conformal_factor, const Scalar<DataType>& lapse,
      51              :     const tnsr::ii<DataType, 3>& conformal_metric,
      52              :     const tnsr::II<DataType, 3>& longitudinal_shift_minus_dt_conformal_metric,
      53              :     const Scalar<DataType>& trace_extrinsic_curvature);
      54              : /// @}
      55              : 
      56              : }  // namespace Xcts