A callable 4D metric class for general relativity (Minkowski, Schwarzschild, Kerr, etc.) More...

#include <Metric.hpp>

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Public Member Functions
	Metric (const std::string &metric_type="minkowski", T mass=T(1.0), T spin=T(0.0))
	Constructor.

void	operator() (const tensorium::Vector< T > &X, tensorium::Tensor< T, 2 > &g) const
	Evaluate the metric tensor \( g_{\mu\nu}(X^\lambda) \).

void	BSSN (const tensorium::Vector< T > &X, T &alpha, tensorium::Vector< T > &beta, tensorium::Tensor< T, 2 > &gamma) const
	Extract BSSN 3+1 variables (lapse, shift, and spatial metric)

T	compute_conformal_factor (const tensorium::Tensor< T, 2 > &gamma) const

void	compute_conformal_metric (const tensorium::Tensor< T, 2 > &gamma, T chi, tensorium::Tensor< T, 2 > &gamma_tilde) const

Public Attributes
std::string	type

T	M = T(1.0)

T	a = T(0.935)

Private Member Functions
void	set_custom (std::function< void(const tensorium::Vector< T > &, tensorium::Tensor< T, 2 > &)> fn)
	Set a custom metric callable function.

void	compute_minkowski (tensorium::Tensor< T, 2 > &g) const
	Minkowski metric in Cartesian coordinates.

void	compute_schwarzschild (const tensorium::Vector< T > &X, tensorium::Tensor< T, 2 > &g) const
	Schwarzschild metric in spherical coordinates.

void	compute_kerr (const tensorium::Vector< T > &X, tensorium::Tensor< T, 2 > &g) const
	Kerr metric in Boyer–Lindquist coordinates.

void	compute_flrw (const tensorium::Vector< T > &X, tensorium::Tensor< T, 2 > &g) const
	Flat FLRW metric in comoving spherical coordinates.

T	kerr_schild_radius (T x, T y, T z) const
	Kerr–Schild radius extraction helper.

void	compute_kerr_schild (const tensorium::Vector< T > &X, tensorium::Tensor< T, 2 > &g) const
	Kerr–Schild metric in Cartesian coordinates.

Private Attributes
std::function< void(const tensorium::Vector< T > &, tensorium::Tensor< T, 2 > &)	custom_metric_fn )
	Optional user-defined metric function (must accept X and fill g)

Detailed Description

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

A callable 4D metric class for general relativity (Minkowski, Schwarzschild, Kerr, etc.)

This class provides access to several pre-implemented metrics (Minkowski, Schwarzschild, Kerr, Kerr–Schild, FLRW), and supports user-defined metrics via a custom callable.

It supports:

Direct evaluation of the metric tensor \( g_{\mu\nu}(X^\lambda) \)
Extraction of ADM variables for BSSN formalism: lapse \( \alpha \), shift \( \beta^i \), and spatial metric \( \gamma_{ij} \)

The class is callable via operator() and adapts to the type of metric selected by type.

Template Parameters

T	Scalar type (e.g., float or double)

Constructor & Destructor Documentation

◆ Metric()

template<typename T >

tensorium_RG::Metric< T >::Metric	(	const std::string &	metric_type = "minkowski",
		T	mass = T(1.0),
		T	spin = T(0.0) )

inline

Constructor.

Parameters

metric_type	Name of the metric ("minkowski", "schwarzschild", "kerr", etc.)
mass	Central mass (default = 1.0)
spin	Spin parameter (only relevant for Kerr/Kerr–Schild)

Member Function Documentation

◆ BSSN()

template<typename T >

void tensorium_RG::Metric< T >::BSSN	(	const tensorium::Vector< T > &	X,
		T &	alpha,
		tensorium::Vector< T > &	beta,
		tensorium::Tensor< T, 2 > &	gamma ) const

inline

Extract BSSN 3+1 variables (lapse, shift, and spatial metric)

Decomposes the 4D metric at point X into ADM form:

\[ ds^2 = -\alpha^2 dt^2 + \gamma_{ij} (dx^i + \beta^i dt)(dx^j + \beta^j dt) \]

Parameters

X	4D coordinate vector \( X^\mu \)
alpha	Output scalar lapse function \( \alpha \)
beta	Output shift vector \( \beta^i \)
gamma	Output 3x3 spatial metric \( \gamma_{ij} \)

References alpha, beta, gamma, and X().

Referenced by tensorium_RG::BSSNContractedGamma< T >::compute(), tensorium_RG::BSSNContractedGamma< T >::compute_contracted_christoffel(), tensorium_RG::RicciTildeTensor< T >::compute_laplacian_term(), tensorium_RG::generate_conformal_metric_field(), and tensorium_RG::BSSN< T >::init_BSSN().

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◆ compute_conformal_factor()

template<typename T >

T tensorium_RG::Metric< T >::compute_conformal_factor ( const tensorium::Tensor< T, 2 > & gamma ) const

inline

References gamma.

Referenced by tensorium::compute_conformal_factor(), tensorium_RG::generate_conformal_metric_field(), and tensorium_RG::BSSN< T >::init_BSSN().

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◆ compute_conformal_metric()

template<typename T >

void tensorium_RG::Metric< T >::compute_conformal_metric	(	const tensorium::Tensor< T, 2 > &	gamma,
		T	chi,
		tensorium::Tensor< T, 2 > &	gamma_tilde ) const