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/Tensor.hpp"
       9             : #include "Utilities/Gsl.hpp"
      10             : 
      11             : namespace gr {
      12             : /// @{
      13             : 
      14             : /*!
      15             :  * \brief Computes the coordinate geodesic acceleration in the inertial frame.
      16             :  *
      17             :  * \details The geodesic acceleration in coordinate form is given by
      18             :  * \f{equation}
      19             :  *  \frac{d^2 x^i}{d t^2} = (v^i \Gamma^0_{00} - \Gamma^i_{00} )  + 2 v^j (v^i
      20             :  * \Gamma^0_{j0} - \Gamma^i_{j0} ) + v^j v^k (v^i \Gamma^0_{jk} - \Gamma^i_{jk}
      21             :  * ), \f}
      22             :  * where \f$v^i\f$ is the coordinate velocity, \f$\Gamma^\mu_{\nu \rho}\f$ are
      23             :  * the spacetime Christoffel symbols of the second kind, and all latin indices
      24             :  * are spatial.
      25             :  */
      26             : template <typename DataType, size_t Dim>
      27           1 : void geodesic_acceleration(
      28             :     gsl::not_null<tnsr::I<DataType, Dim>*> acceleration,
      29             :     const tnsr::I<DataType, Dim>& velocity,
      30             :     const tnsr::Abb<DataType, Dim>& christoffel_second_kind);
      31             : 
      32             : template <typename DataType, size_t Dim>
      33           1 : tnsr::I<DataType, Dim> geodesic_acceleration(
      34             :     const tnsr::I<DataType, Dim>& velocity,
      35             :     const tnsr::Abb<DataType, Dim>& christoffel_second_kind);
      36             : /// @}
      37             : 
      38             : }  // namespace gr