tensorium_RG::BSSNChristoffel< T > Class Template Reference

Compute the conformal Christoffel symbols \( \tilde{\Gamma}^k_{ij} \). More...

#include <BSSNChristoffel.hpp>

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Static Public Member Functions
static void	compute (const tensorium::Tensor< T, 2 > &gamma_tilde, const tensorium::Tensor< T, 3 > &dgamma_tilde, const tensorium::Tensor< T, 2 > &gamma_tilde_inv, tensorium::Tensor< T, 3 > &Christoffel)
	Compute the conformal Christoffel symbols \( \tilde{\Gamma}^k_{ij} \).

Detailed Description

template<typename T>
class tensorium_RG::BSSNChristoffel< T >

Compute the conformal Christoffel symbols \( \tilde{\Gamma}^k_{ij} \).

The conformal Christoffel symbols are computed from the inverse conformal metric \( \tilde{\gamma}^{kl} \) and the derivatives of the conformal metric \( \partial_m \tilde{\gamma}_{ij} \) using the formula:

\[ \tilde{\Gamma}^k_{ij} = \frac{1}{2} \tilde{\gamma}^{kl} \left( \partial_i \tilde{\gamma}_{jl} + \partial_j \tilde{\gamma}_{il} - \partial_l \tilde{\gamma}_{ij} \right) \]

Member Function Documentation

compute()

template<typename T >

static void tensorium_RG::BSSNChristoffel< T >::compute ( const tensorium::Tensor< T, 2 > & gamma_tilde, const tensorium::Tensor< T, 3 > & dgamma_tilde, const tensorium::Tensor< T, 2 > & gamma_tilde_inv, tensorium::Tensor< T, 3 > & Christoffel )

inlinestatic

Compute the conformal Christoffel symbols \( \tilde{\Gamma}^k_{ij} \).

Parameters

gamma_tilde	3×3 conformal metric \( \tilde{\gamma}_{ij} \)
dgamma_tilde	3×3×3 partial derivatives \( \partial_k \tilde{\gamma}_{ij} \)
gamma_tilde_inv	3×3 inverse metric \( \tilde{\gamma}^{ij} \)
Christoffel	Output: \( \tilde{\Gamma}^k_{ij} \)

References tensorium::Tensor< K, Rank >::resize(), and tensorium::Tensor< K, Rank >::shape().

Referenced by tensorium::compute_christoffel_3D().

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The documentation for this class was generated from the following file:

• includes/Tensorium/DiffGeometry/BSSN/BSSNChristoffel.hpp