tensorium_RG::TildeGamma< T > Class Template Reference

Computes the contracted conformal Christoffel vector \( \tilde{\Gamma}^i \). More...

#include <BSSNTildeChristoffel.hpp>

Collaboration diagram for tensorium_RG::TildeGamma< T >:

Static Public Member Functions
static void	compute (const tensorium::Tensor< T, 2 > &gamma_tilde_inv, const tensorium::Tensor< T, 3 > &christoffel, tensorium::Vector< T > &tildeGamma)
	Computes \( \tilde{\Gamma}^i = \tilde{\gamma}^{jk} \tilde{\Gamma}^i_{jk} \).

Detailed Description

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

Computes the contracted conformal Christoffel vector \( \tilde{\Gamma}^i \).

The BSSN formalism requires computing the vector:

\[ \tilde{\Gamma}^i = \tilde{\gamma}^{jk} \tilde{\Gamma}^i_{jk} \]

where:

• \( \tilde{\gamma}^{jk} \) is the inverse of the conformal 3-metric
• \( \tilde{\Gamma}^i_{jk} \) are the Christoffel symbols computed from the conformal metric

This quantity is key in the evolution of the conformal connection functions in the BSSN system.

Template Parameters

T	Type used for floating-point computations (usually double)

Member Function Documentation

compute()

template<typename T >

static void tensorium_RG::TildeGamma< T >::compute ( const tensorium::Tensor< T, 2 > & gamma_tilde_inv, const tensorium::Tensor< T, 3 > & christoffel, tensorium::Vector< T > & tildeGamma )

inlinestatic

Computes \( \tilde{\Gamma}^i = \tilde{\gamma}^{jk} \tilde{\Gamma}^i_{jk} \).

This function contracts the conformal Christoffel symbols \( \tilde{\Gamma}^i_{jk} \) with the inverse conformal metric \( \tilde{\gamma}^{jk} \) to yield the vector:

\[ \tilde{\Gamma}^i = \tilde{\gamma}^{jk} \tilde{\Gamma}^i_{jk} \]

Parameters

gamma_tilde_inv	A 3×3 tensor representing \( \tilde{\gamma}^{jk} \)
christoffel	A 3×3×3 tensor containing the Christoffel symbols \( \tilde{\Gamma}^i_{jk} \)
tildeGamma	Output vector of size 3, storing \( \tilde{\Gamma}^i \)

Exceptions

std::invalid_argument

if tensor dimensions are incorrect

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

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

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