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 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