tensorium_RG::Metric< T > Class Template Reference

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 ) = nullptr
	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::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_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 chi, gamma, and tensorium::Tensor< K, Rank >::resize().

Referenced by 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(), theta, and X().

Referenced by tensorium_RG::Metric< T >::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 tensorium_RG::Metric< T >::a, Delta, tensorium::Tensor< K, Rank >::fill(), tensorium_RG::Metric< T >::M, tensorium::Tensor< K, Rank >::resize(), Sigma, theta, and X().

Referenced by tensorium_RG::Metric< T >::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 tensorium_RG::Metric< T >::a, tensorium::Tensor< K, Rank >::fill(), tensorium_RG::Metric< T >::kerr_schild_radius(), tensorium_RG::Metric< T >::M, mu, nu, tensorium::Tensor< K, Rank >::resize(), and X().

Referenced by tensorium_RG::Metric< T >::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 tensorium_RG::Metric< T >::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 f(), tensorium::Tensor< K, Rank >::fill(), tensorium_RG::Metric< T >::M, tensorium::Tensor< K, Rank >::resize(), theta, and X().

Referenced by tensorium_RG::Metric< T >::operator()().

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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 tensorium_RG::Metric< T >::a.

Referenced by tensorium_RG::Metric< T >::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 tensorium_RG::Metric< T >::compute_flrw(), tensorium_RG::Metric< T >::compute_kerr(), tensorium_RG::Metric< T >::compute_kerr_schild(), tensorium_RG::Metric< T >::compute_minkowski(), tensorium_RG::Metric< T >::compute_schwarzschild(), tensorium_RG::Metric< T >::custom_metric_fn, tensorium_RG::Metric< T >::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 tensorium_RG::Metric< T >::custom_metric_fn, and tensorium_RG::Metric< T >::type.

Member Data Documentation

a

template<typename T >

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

Referenced by tensorium_RG::Metric< T >::compute_kerr(), tensorium_RG::Metric< T >::compute_kerr_schild(), and tensorium_RG::Metric< T >::kerr_schild_radius().

custom_metric_fn

template<typename T >

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

private

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

Referenced by tensorium_RG::Metric< T >::operator()(), and tensorium_RG::Metric< T >::set_custom().

M

template<typename T >

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

Referenced by tensorium_RG::Metric< T >::compute_kerr(), tensorium_RG::Metric< T >::compute_kerr_schild(), and tensorium_RG::Metric< T >::compute_schwarzschild().

type

template<typename T >

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

Referenced by tensorium_RG::Metric< T >::operator()(), and tensorium_RG::Metric< T >::set_custom().

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

• includes/Tensorium/DiffGeometry/Metric.hpp