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/DataBox/Tag.hpp"
       9             : #include "DataStructures/Tensor/TypeAliases.hpp"
      10             : #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
      11             : #include "Utilities/TMPL.hpp"
      12             : 
      13             : /// \cond
      14             : namespace gsl {
      15             : template <typename>
      16             : struct not_null;
      17             : }  // namespace gsl
      18             : /// \endcond
      19             : 
      20             : namespace gr {
      21             : 
      22             : /// @{
      23             : /*!
      24             :  * \brief Computes the Pontryagin scalar in vacuum.
      25             :  *
      26             :  * \details The Pontryagin scalar in vacuum is given by
      27             :  * \begin{align}
      28             :  *   \mathcal{P} &\equiv {^{\star} C}_{abcd} C^{abcd} \\
      29             :  *    &= - 16 E_{ab} B^{ab} ~,
      30             :  * \end{align}
      31             :  * where $ C_{abcd} $ it the Weyl tensor (with dual $ {^\star} C}_{abcd} $) in 4
      32             :  * spacetime dimensions. Here it is computed in terms of the electric ($
      33             :  * E_{ab} $) and magnetic ($ B_{ab} $) parts of the Weyl scalar, with the
      34             :  * conventions used here for ($ \{E_{ab}, B_{ab}\} $).
      35             :  *
      36             :  * \see `gr::Tags::WeylMagnetic` and `gr::Tags::WeylElectric`
      37             :  *
      38             :  */
      39             : template <typename Frame>
      40           1 : void pontryagin_scalar_in_vacuum(
      41             :     gsl::not_null<Scalar<DataVector>*> pontryagin_scalar,
      42             :     const tnsr::ii<DataVector, 3, Frame>& weyl_electric,
      43             :     const tnsr::ii<DataVector, 3, Frame>& weyl_magnetic,
      44             :     const tnsr::II<DataVector, 3, Frame>& inverse_spatial_metric);
      45             : 
      46             : template <typename Frame>
      47           1 : Scalar<DataVector> pontryagin_scalar_in_vacuum(
      48             :     const tnsr::ii<DataVector, 3, Frame>& weyl_electric,
      49             :     const tnsr::ii<DataVector, 3, Frame>& weyl_magnetic,
      50             :     const tnsr::II<DataVector, 3, Frame>& inverse_spatial_metric);
      51             : /// @}
      52             : 
      53             : /// @{
      54             : /*!
      55             :  * \brief Computes Gauss-Bonnet scalar in vacuum.
      56             :  *
      57             :  * \details The Gauss-Bonnet scalar in vacuum is given by
      58             :  * \begin{align}
      59             :  *   \mathcal{G} &\equiv R_{abcd} R^{abcd} - 4 R_{ab} R^{ab} + R^2
      60             :  *    &= C_{abcd} C^{abcd}
      61             :  *    &= 8 (E_{ab} E^{ab} - B_{ab} B^{ab}) ~,
      62             :  * \end{align}
      63             :  * where $ R_{abcd} $, $ R_{ab} $, $ R $ $ C_{abcd} $ are the Riemann tensor,
      64             :  * Ricci tensor, Ricci scalar and Weyl tensor in 4 spacetime dimensions. The
      65             :  * Gauss-Bonnet scalar in vacuum can be computed in terms of the electric ($
      66             :  * E_{ab} $) and magnetic ($ B_{ab} $) parts of the Weyl tensor.
      67             :  *
      68             :  * \see `gr::Tags::WeylMagnetic` and `gr::Tags::WeylElectric`
      69             :  *
      70             :  */
      71           1 : void gauss_bonnet_scalar_in_vacuum(
      72             :     gsl::not_null<Scalar<DataVector>*> gb_scalar,
      73             :     const Scalar<DataVector>& weyl_electric_scalar,
      74             :     const Scalar<DataVector>& weyl_magnetic_scalar);
      75             : 
      76           1 : Scalar<DataVector> gauss_bonnet_scalar_in_vacuum(
      77             :     const Scalar<DataVector>& weyl_electric_scalar,
      78             :     const Scalar<DataVector>& weyl_magnetic_scalar);
      79             : /// @}
      80             : 
      81             : }  // namespace gr