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

#include <Metric.hpp>

Collaboration diagram for tensorium_RG::Metric< T >:

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.
tensorium::Vector< T >	convert_to_metric_coordinates (const tensorium::Vector< T > &X) const
tensorium::Tensor< T, 2 >	invert_metric_tensor (const tensorium::Tensor< T, 2 > &g) const
tensorium::Tensor< T, 2 >	invert_spatial_metric (const tensorium::Tensor< T, 2 > &gamma) const
void	validate_adm_split (const tensorium::Tensor< T, 2 > &g, const tensorium::Tensor< T, 2 > &gamma, const tensorium::Vector< T > &beta, T alpha) const

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)

References a, M, and type.

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 convert_to_metric_coordinates(), invert_metric_tensor(), invert_spatial_metric(), tensorium::Tensor< K, Rank >::resize(), tensorium::Vector< K >::resize(), validate_adm_split(), and X().

Referenced by tensorium_RG::BSSNContractedGamma< T >::compute(), tensorium_RG::ChiContext< T >::compute(), tensorium_RG::BSSNContractedGamma< T >::compute_contracted_christoffel(), tensorium_RG::compute_dt_gamma_from_metric(), tensorium_RG::RicciTildeTensor< T >::compute_laplacian_term(), tensorium_RG::generate_conformal_metric_field(), tensorium_RG::BSSN< T >::init_BSSN(), and tensorium_RG::bssn::split_3p1().

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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 tensorium::Tensor< K, Rank >::dimensions.

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

inline

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

Referenced by tensorium::compute_conformal_metric(), and tensorium_RG::generate_conformal_metric_field().

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◆ compute_flrw()

template<typename T>

void tensorium_RG::Metric< T >::compute_flrw	(	const tensorium::Vector< T > &	X,
		tensorium::Tensor< T, 2 > &	g ) const

inlineprivate

Flat FLRW metric in comoving spherical coordinates.

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

Referenced by operator()().

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◆ compute_kerr()

template<typename T>

void tensorium_RG::Metric< T >::compute_kerr	(	const tensorium::Vector< T > &	X,
		tensorium::Tensor< T, 2 > &	g ) const

inlineprivate

Kerr metric in Boyer–Lindquist coordinates.

References a, tensorium::Tensor< K, Rank >::fill(), M, tensorium::Tensor< K, Rank >::resize(), and X().

Referenced by operator()().

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◆ compute_kerr_schild()

template<typename T>

void tensorium_RG::Metric< T >::compute_kerr_schild	(	const tensorium::Vector< T > &	X,
		tensorium::Tensor< T, 2 > &	g ) const

inlineprivate

Kerr–Schild metric in Cartesian coordinates.

References a, tensorium::Tensor< K, Rank >::fill(), kerr_schild_radius(), M, tensorium::Tensor< K, Rank >::resize(), and X().

Referenced by operator()().

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◆ compute_minkowski()

template<typename T>

void tensorium_RG::Metric< T >::compute_minkowski ( tensorium::Tensor< T, 2 > & g ) const

inlineprivate

Minkowski metric in Cartesian coordinates.

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

Referenced by operator()().

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◆ compute_schwarzschild()

template<typename T>

void tensorium_RG::Metric< T >::compute_schwarzschild	(	const tensorium::Vector< T > &	X,
		tensorium::Tensor< T, 2 > &	g ) const

inlineprivate

Schwarzschild metric in spherical coordinates.

References tensorium::Tensor< K, Rank >::fill(), M, tensorium::Tensor< K, Rank >::resize(), and X().

Referenced by operator()().

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◆ convert_to_metric_coordinates()

template<typename T>

tensorium::Vector< T > tensorium_RG::Metric< T >::convert_to_metric_coordinates ( const tensorium::Vector< T > & X ) const

inlineprivate

References type, and X().

Referenced by BSSN().

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◆ invert_metric_tensor()

template<typename T>

tensorium::Tensor< T, 2 > tensorium_RG::Metric< T >::invert_metric_tensor ( const tensorium::Tensor< T, 2 > & g ) const

inlineprivate

References tensorium::Tensor< K, Rank >::dimensions, and tensorium::Matrix< K, RowMajor >::inverse().

Referenced by BSSN().

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◆ invert_spatial_metric()

template<typename T>

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

inlineprivate

References tensorium::Matrix< K, RowMajor >::inverse().

Referenced by BSSN().

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◆ kerr_schild_radius()

template<typename T>

T tensorium_RG::Metric< T >::kerr_schild_radius	(	T	x,
		T	y,
		T	z ) const

inlineprivate

Kerr–Schild radius extraction helper.

References a.

Referenced by compute_kerr_schild().

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◆ operator()()

template<typename T>

void tensorium_RG::Metric< T >::operator()	(	const tensorium::Vector< T > &	X,
		tensorium::Tensor< T, 2 > &	g ) const

inline

Evaluate the metric tensor \( g_{\mu\nu}(X^\lambda) \).

Dispatches to the appropriate metric implementation based on type. Throws an exception if the type is unknown and no custom function is set.

Parameters

X	4D coordinate vector \( (t, r, \theta, \phi) \) or Cartesian if Kerr–Schild
g	Output tensor to be filled with \( g_{\mu\nu} \)

References compute_flrw(), compute_kerr(), compute_kerr_schild(), compute_minkowski(), compute_schwarzschild(), custom_metric_fn, type, and X().

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◆ set_custom()

template<typename T>

void tensorium_RG::Metric< T >::set_custom ( std::function< void(const tensorium::Vector< T > &, tensorium::Tensor< T, 2 > &)> fn )

inlineprivate

Set a custom metric callable function.

References custom_metric_fn, and type.

◆ validate_adm_split()

template<typename T>

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

inlineprivate

References tensorium::Tensor< K, Rank >::fill().

Referenced by BSSN().

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Member Data Documentation

◆ a

template<typename T>

T tensorium_RG::Metric< T >::a = T(0.935)

Referenced by compute_kerr(), compute_kerr_schild(), kerr_schild_radius(), and Metric().

◆ custom_metric_fn

template<typename T>

std::function<void(const tensorium::Vector<T> &, tensorium::Tensor<T, 2> &)> tensorium_RG::Metric< T >::custom_metric_fn

private

Initial value:

=

nullptr

Optional user-defined metric function (must accept X and fill g).

Referenced by operator()(), and set_custom().

◆ M

template<typename T>

T tensorium_RG::Metric< T >::M = T(1.0)

Referenced by compute_kerr(), compute_kerr_schild(), compute_schwarzschild(), and Metric().

◆ type

template<typename T>

std::string tensorium_RG::Metric< T >::type

Referenced by convert_to_metric_coordinates(), Metric(), operator()(), and set_custom().

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

includes/Tensorium/Physics/DiffGeometry/Metric.hpp

Public Member Functions

Public Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Metric()

Member Function Documentation

◆ BSSN()

◆ compute_conformal_factor()

◆ compute_conformal_metric()

◆ compute_flrw()

◆ compute_kerr()

◆ compute_kerr_schild()

◆ compute_minkowski()

◆ compute_schwarzschild()

◆ convert_to_metric_coordinates()

◆ invert_metric_tensor()

◆ invert_spatial_metric()

◆ kerr_schild_radius()

◆ operator()()

◆ set_custom()

◆ validate_adm_split()

Member Data Documentation

◆ a

◆ custom_metric_fn

◆ M

◆ type