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 Ccz4 {
      12              : /// @{
      13              : /*!
      14              :  * \brief Computes the gradient of the gradient of the lapse.
      15              :  *
      16              :  * \details Computes the gradient of the gradient as:
      17              :  * \f{align}
      18              :  *     \nabla_i \nabla_j \alpha &= \alpha A_i A_j -
      19              :  *                 \alpha \Gamma^k{}_{ij} A_k + \alpha \partial_{(i} A_{j)}
      20              :  * \f}
      21              :  * where \f$\alpha\f$, \f$\Gamma^k{}_{ij}\f$, \f$A_i\f$, and
      22              :  * \f$\partial_j A_i\f$ are the lapse, spatial christoffel symbols of the second
      23              :  * kind, the CCZ4 auxiliary variable defined by `Ccz4::Tags::FieldA`, and its
      24              :  * spatial derivative, respectively.
      25              :  *
      26              :  * \note In second-order Ccz4, we impose symmetry of index i and j
      27              :  * in \f$ \partial_i A_j=\partial_i \partial_j \ln \alpha \f$,
      28              :  * because partial derivatives commute and to use
      29              :  * `second_partial_derivatives()`. \f$ A_i \f$ is evolved in
      30              :  * the first-order system so no such symmetry is imposed.
      31              :  */
      32              : template <typename DataType, size_t Dim, typename Frame, typename TensorType>
      33            1 : void grad_grad_lapse(
      34              :     const gsl::not_null<tnsr::ij<DataType, Dim, Frame>*> result,
      35              :     const Scalar<DataType>& lapse,
      36              :     const tnsr::Ijj<DataType, Dim, Frame>& christoffel_second_kind,
      37              :     const tnsr::i<DataType, Dim, Frame>& field_a, const TensorType& d_field_a);
      38              : 
      39              : template <typename DataType, size_t Dim, typename Frame, typename TensorType>
      40            1 : tnsr::ij<DataType, Dim, Frame> grad_grad_lapse(
      41              :     const Scalar<DataType>& lapse,
      42              :     const tnsr::Ijj<DataType, Dim, Frame>& christoffel_second_kind,
      43              :     const tnsr::i<DataType, Dim, Frame>& field_a, const TensorType& d_field_a);
      44              : 
      45              : /// @}
      46              : 
      47              : /// @{
      48              : /*!
      49              :  * \ingroup GeneralRelativityGroup
      50              :  * \brief Computes the divergence of the lapse.
      51              :  *
      52              :  * \details Computes the divergence as:
      53              :  * \f{align}
      54              :  *     \nabla^i \nabla_i \alpha &= \phi^2 \tilde{\gamma}^{ij}
      55              :  *         (\nabla_i \nabla_j \alpha)
      56              :  * \f}
      57              :  * where \f$\phi\f$, \f$\tilde{\gamma}^{ij}\f$, and
      58              :  * \f$\nabla_i \nabla_j \alpha\f$ are the conformal factor, inverse conformal
      59              :  * spatial metric, and the gradient of the gradient of the lapse defined by
      60              :  * `Ccz4::Tags::ConformalFactor`, `Ccz4::Tags::InverseConformalMetric`, and
      61              :  * `Ccz4::Tags::GradGradLapse`, respectively.
      62              :  */
      63              : template <typename DataType, size_t Dim, typename Frame>
      64            1 : void divergence_lapse(
      65              :     const gsl::not_null<Scalar<DataType>*> result,
      66              :     const Scalar<DataType>& conformal_factor_squared,
      67              :     const tnsr::II<DataType, Dim, Frame>& inverse_conformal_metric,
      68              :     const tnsr::ij<DataType, Dim, Frame>& grad_grad_lapse);
      69              : 
      70              : template <typename DataType, size_t Dim, typename Frame>
      71            1 : Scalar<DataType> divergence_lapse(
      72              :     const Scalar<DataType>& conformal_factor_squared,
      73              :     const tnsr::II<DataType, Dim, Frame>& inverse_conformal_metric,
      74              :     const tnsr::ij<DataType, Dim, Frame>& grad_grad_lapse);
      75              : /// @}
      76              : }  // namespace Ccz4