Class to manage asymptotically anti de Sitter metrics. More...

#include <metric_AADS.hpp>

Inheritance diagram for Kadath::Metric_AADS:

Public Member Functions
	Metric_AADS (const Space &space, Metric_tensor &hmet)
	Standard constructor. More...

	Metric_AADS (const Metric_AADS &so)
	Copy constructor. More...

virtual void	manipulate_ind (Term_eq &so, int ind) const
	Uses the `Metric` to manipulate one of the index of a `Term_eq` (i.e. More...

virtual Term_eq	derive (int type_der, char ind_der, const Term_eq &so) const
	Computes the covariant derivative of a `Term_eq` (assumes Cartesian basis of decomposition). More...

void	set_system (System_of_eqs &syst, const char name_met, const char name_hmet)
	Associates the metric to a given system of equations. More...

void	set_system (System_of_eqs &syst, const char name_met, const char name_hmet, const char name_back_cov, const char name_back_con, const char *name_back_ricci)
	Associates the metric to a given system of equations. More...

void	set_system (System_of_eqs &syst, const char name_met, const char name_hmet, const char name_back_cov, const char name_back_con, const char name_back_gam, const char name_back_ricci)
	Associates the metric to a given system of equations. More...

virtual const Metric *	get_background () const

virtual Term_eq	derive_partial (int typeder, char nameder, const Term_eq &so) const
	Computes the partial derivative of a `Term_eq` (assumes Cartesian basis of decomposition). More...

virtual Term_eq	derive_flat (int typeder, char nameder, const Term_eq &so) const
	Computes the covariant flat derivative of a `Term_eq`. More...

virtual int	give_type (int) const
	Returns the type of tensorial basis of the covariant representation, in a given `Domain`. More...

const Term_eq *	give_term (int typemet, int dd) const
	Gives one representation of the metric, in a `Domain`. More...

const Term_eq *	give_christo (int dd) const
	Gives the Christoffel symbols, in a `Domain`. More...

const Term_eq *	give_riemann (int dd) const
	Gives the Riemann tensor, in a `Domain`. More...

const Term_eq *	give_ricci_tensor (int dd) const
	Gives the Ricci tensor, in a `Domain`. More...

const Term_eq *	give_ricci_scalar (int dd) const
	Gives the Ricci scalar, in a `Domain`. More...

const Term_eq *	give_dirac (int dd) const
	Gives the potential of the Dirac gauge, in a `Domain`. More...

const Term_eq *	give_det_cov (int dd) const
	Gives the determinant of the covariant metric, in a `Domain`. More...

Protected Member Functions
virtual void	compute_cov (int d) const
	Computes the covariant representation, in a given `Domain`. More...

virtual void	compute_con (int d) const
	Computes the contravariant representation, in a given `Domain`. More...

virtual void	compute_christo (int d) const
	Computes the Christoffel symbols, in a given `Domain`. More...

virtual void	compute_ricci_tensor (int d) const
	Computes the Ricci tensor, in a given `Domain`. More...

virtual void	compute_ricci_scalar (int d) const
	Computes the Ricci scalar, in a given `Domain`. More...

virtual void	update (int d)
	Updates the derived quantities (Christoffels etc..) in a given `Domain` This is done only for the ones that are needed, i.e. More...

virtual void	update ()
	Updates the derived quantities (Christoffels etc..) This is done only for the ones that are needed, i.e. More...

virtual void	compute_riemann (int) const
	Computes the Riemann tensor, in a given `Domain`. More...

virtual void	compute_dirac (int) const
	Computes the Dirac gauge term, in a given `Domain`. More...

virtual void	compute_det_cov (int) const
	Computes the determinant of the covariant representation, in a given `Domain`. More...

Protected Attributes
int	m_nd
	number of physical domains (usually the last compaxtified domain is discarded). More...

int	m_place_syst
	Where is the unknown h in the system of equations. More...

double	m_L
	AdS length. More...

bool	m_doder
	true if metric variation allowed to be computed More...

Metric_ADS	m_ads
	Background metric(i.e. ADS metric). More...

Metric_tensor *	p_hmet
	$h_{ij}$ : the discrepancy between covariant metric and contravariant background. More...

Vector *	p_der_eps
	Pointer on the vector containing the derivative of the conformal factor $D_i \epsilon$ . More...

Base_tensor *	p_basis
	Pointer on the tensorial basis (Cartesian basis only). More...

const Space &	espace
	The associated `Space`. More...

const System_of_eqs *	syst
	Pointer of the system of equations where the metric is used (only one for now). More...

MMPtr_array< Term_eq >	p_met_cov
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_met_con
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_christo
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_riemann
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_ricci_tensor
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_ricci_scalar
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_dirac
	Array of pointers on various `Term_eq`. More...

MMPtr_array< Term_eq >	p_det_cov
	Array of pointers on various `Term_eq`. More...

int	type_tensor
	States if one works in the CON or COV representation. More...

Private Member Functions
Term_eq	derive_simple (const Term_eq &so) const
	Computes the covariant derivative. More...

Private Attributes
Term_eq **	p_h
	Pointers on the differences between the covariant metric and the covariant background. More...

Term_eq **	p_k
	Pointers on the differences between the contravariant metric and the contravariant background. More...

Detailed Description

Class to manage asymptotically anti de Sitter metrics.

Definition at line 128 of file metric_AADS.hpp.

Constructor & Destructor Documentation

◆ Metric_AADS() [1/2]

Kadath::Metric_AADS::Metric_AADS	(	const Space &	space,
		Metric_tensor &	hmet
	)

Standard constructor.

Parameters

space	: the associated `Space`.
hmet	: the difference between the covariant metric and the covariant background

Definition at line 22 of file metric_AADS.cpp.

References Kadath::Metric::espace, Kadath::Domain::get_cart(), Kadath::Space::get_domain(), Kadath::Space::get_nbr_domains(), Kadath::Space::get_ndim(), Kadath::Domain::get_rmax(), Kadath::Metric_tensor::get_type(), m_ads, m_L, m_nd, Kadath::Metric_ADS::m_rho2, p_basis, p_der_eps, p_h, p_k, Kadath::Vector::set(), Kadath::Scalar::set_domain(), and Kadath::Metric::type_tensor.

◆ Metric_AADS() [2/2]

Kadath::Metric_AADS::Metric_AADS ( const Metric_AADS & so )

Copy constructor.

Definition at line 48 of file metric_AADS.cpp.

References Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), m_nd, p_basis, p_der_eps, p_h, p_hmet, and p_k.

Member Function Documentation

◆ compute_christo()

void Kadath::Metric_AADS::compute_christo ( int dd ) const

protectedvirtual

Computes the Christoffel symbols, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 290 of file metric_AADS.cpp.

References Kadath::Index::inc(), Kadath::Tensor::set(), Kadath::Array< T >::set(), and Kadath::Scalar::set_domain().

◆ compute_con()

void Kadath::Metric_AADS::compute_con ( int ) const

protectedvirtual

Computes the contravariant representation, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 113 of file metric_AADS.cpp.

References Kadath::Term_eq::get_der_t(), Kadath::Term_eq::get_val_t(), Kadath::Tensor::set(), and Kadath::Scalar::set_domain().

◆ compute_cov()

void Kadath::Metric_AADS::compute_cov ( int ) const

protectedvirtual

Computes the covariant representation, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 92 of file metric_AADS.cpp.

◆ compute_det_cov()

void Kadath::Metric::compute_det_cov ( int ) const

protectedvirtualinherited

Computes the determinant of the covariant representation, in a given Domain.

Reimplemented in Kadath::Metric_harmonic.

Definition at line 750 of file metric.cpp.

◆ compute_dirac()

void Kadath::Metric::compute_dirac ( int ) const

protectedvirtualinherited

Computes the Dirac gauge term, in a given Domain.

Reimplemented in Kadath::Metric_conf, and Kadath::Metric_general.

Definition at line 745 of file metric.cpp.

◆ compute_ricci_scalar()

void Kadath::Metric_AADS::compute_ricci_scalar ( int dd ) const

protectedvirtual

Computes the Ricci scalar, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 521 of file metric_AADS.cpp.

References Kadath::Scalar::set_domain().

◆ compute_ricci_tensor()

void Kadath::Metric_AADS::compute_ricci_tensor ( int dd ) const

protectedvirtual

Computes the Ricci tensor, in a given Domain.

Reimplemented from Kadath::Metric.

Definition at line 463 of file metric_AADS.cpp.

References Kadath::Index::inc(), Kadath::Tensor::set(), and Kadath::Scalar::set_domain().

◆ compute_riemann()

void Kadath::Metric::compute_riemann ( int dd ) const

protectedvirtualinherited

Computes the Riemann tensor, in a given Domain.

Reimplemented in Kadath::Metric_nophi_AADS, Kadath::Metric_nophi, Kadath::Metric_cfc, Kadath::Metric_conf_factor, Kadath::Metric_conf, Kadath::Metric_general, and Kadath::Metric_ADS.

Definition at line 476 of file metric.cpp.

References Kadath::Metric::compute_christo(), Kadath::Val_domain::der_abs(), Kadath::Metric::espace, Kadath::Space::get_domain(), Kadath::Space::get_ndim(), Kadath::Index::inc(), Kadath::Metric::p_christo, Kadath::Metric::p_met_con, Kadath::Metric::p_met_cov, Kadath::Metric::p_riemann, Kadath::Tensor::set(), Kadath::Array< T >::set(), and Kadath::Scalar::set_domain().

◆ derive()

Term_eq Kadath::Metric_AADS::derive	(	int	typeder,
		char	nameder,
		const Term_eq &	so
	)		const

virtual

Computes the covariant derivative of a Term_eq (assumes Cartesian basis of decomposition).

The index corresponding to the derivation is given a name. If need be inner summation is performed.

Parameters

typeder	: the result is either or
nameder	: the name given as the derivation index.
so	: the `Term_eq` to be derived.

Returns: : the covariant derivative.

Reimplemented from Kadath::Metric.

Definition at line 418 of file metric_AADS.cpp.

References Kadath::Term_eq::der_t, Kadath::Tensor::do_summation_one_dom(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), and Kadath::Term_eq::val_t.

◆ derive_flat()

Term_eq Kadath::Metric::derive_flat	(	int	typeder,
		char	nameder,
		const Term_eq &	so
	)		const

virtualinherited

Computes the covariant flat derivative of a Term_eq.

The index corresponding to the derivation is given a name. If need be inner summation is performed.

Parameters

typeder	: the result is either $\bar{D}_i$ or $\bar{D}^i$
nameder	: the name given as the derivation index.
so	: the `Term_eq` to be derived.

Returns: : the covariant flat derivative.

Reimplemented in Kadath::Metric_nophi_AADS, Kadath::Metric_nophi, Kadath::Metric_cfc, Kadath::Metric_conf_factor, Kadath::Metric_conf, and Kadath::Metric_general.

Definition at line 402 of file metric.cpp.

◆ derive_partial()

Term_eq Kadath::Metric::derive_partial	(	int	typeder,
		char	nameder,
		const Term_eq &	so
	)		const

virtualinherited

Computes the partial derivative of a Term_eq (assumes Cartesian basis of decomposition).

The index corresponding to the derivation is given a name. If need be inner summation is performed.

Parameters

typeder	: the result is either $\partial_i$ or $\partial^i$
nameder	: the name given as the derivation index.
so	: the `Term_eq` to be derived.

Returns: : the derivative.

Reimplemented in Kadath::Metric_flat_nophi, and Kadath::Metric_flat.

Definition at line 172 of file metric.cpp.

References Kadath::Metric::compute_con(), Kadath::Metric::compute_cov(), Kadath::Term_eq::der_t, Kadath::Tensor::do_summation_one_dom(), Kadath::Metric::espace, Kadath::Tensor::get_basis(), Kadath::Base_tensor::get_basis(), Kadath::Term_eq::get_dom(), Kadath::Tensor::get_index_type(), Kadath::Tensor::get_name_ind(), Kadath::Term_eq::get_type_data(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::is_name_affected(), Kadath::Metric::manipulate_ind(), Kadath::Metric::p_met_con, Kadath::Metric::p_met_cov, Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Scalar::set_domain(), Kadath::Tensor::set_name_affected(), Kadath::Tensor::set_name_ind(), Kadath::Metric::type_tensor, and Kadath::Term_eq::val_t.

◆ derive_simple()

Term_eq Kadath::Metric_AADS::derive_simple ( const Term_eq & so ) const

private

Computes the covariant derivative.

The name of the index is not defined (hence no inner summation is performed).

Parameters

so	: the `Term_eq` to be derived.

Returns: : the covariant derivative.

Definition at line 363 of file metric_AADS.cpp.

References Kadath::Term_eq::der_t, Kadath::Tensor::get_index_type(), Kadath::Tensor::get_valence(), Kadath::Index::inc(), Kadath::Tensor::set(), Kadath::Index::set(), Kadath::Term_eq::set_der_zero(), Kadath::Scalar::set_domain(), Kadath::Index::set_start(), and Kadath::Term_eq::val_t.

◆ get_background()

const Metric * Kadath::Metric_AADS::get_background ( ) const

virtual

Returns: the pointer on the background metric.

Reimplemented from Kadath::Metric.

Definition at line 609 of file metric_AADS.cpp.

References m_ads.

◆ give_christo()

const Term_eq * Kadath::Metric::give_christo ( int dd ) const

inherited

Gives the Christoffel symbols, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 124 of file metric.cpp.

References Kadath::Metric::compute_christo(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_christo.

◆ give_det_cov()

const Term_eq * Kadath::Metric::give_det_cov ( int dd ) const

inherited

Gives the determinant of the covariant metric, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 159 of file metric.cpp.

References Kadath::Metric::compute_det_cov(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_det_cov.

◆ give_dirac()

const Term_eq * Kadath::Metric::give_dirac ( int dd ) const

inherited

Gives the potential of the Dirac gauge, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 152 of file metric.cpp.

References Kadath::Metric::compute_dirac(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_dirac.

◆ give_ricci_scalar()

const Term_eq * Kadath::Metric::give_ricci_scalar ( int dd ) const

inherited

Gives the Ricci scalar, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 145 of file metric.cpp.

References Kadath::Metric::compute_ricci_scalar(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_ricci_scalar.

◆ give_ricci_tensor()

const Term_eq * Kadath::Metric::give_ricci_tensor ( int dd ) const

inherited

Gives the Ricci tensor, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 138 of file metric.cpp.

References Kadath::Metric::compute_ricci_tensor(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_ricci_tensor.

◆ give_riemann()

const Term_eq * Kadath::Metric::give_riemann ( int dd ) const

inherited

Gives the Riemann tensor, in a Domain.

This is the Term_eq version.

Parameters

dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 131 of file metric.cpp.

References Kadath::Metric::compute_riemann(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), and Kadath::Metric::p_riemann.

◆ give_term()

const Term_eq * Kadath::Metric::give_term	(	int	typemet,
		int	dd
	)		const

inherited

Gives one representation of the metric, in a Domain.

This is the Term_eq version.

Parameters

typemet	: CON or COV.
dd	: in which `Domain`.

Returns: : pointer on the result (being a Term_eq).

Definition at line 103 of file metric.cpp.

References Kadath::Metric::compute_con(), Kadath::Metric::compute_cov(), Kadath::Metric::espace, Kadath::Space::get_nbr_domains(), Kadath::Metric::p_met_con, and Kadath::Metric::p_met_cov.

◆ give_type()

int Kadath::Metric::give_type ( int dd ) const

virtualinherited

Returns the type of tensorial basis of the covariant representation, in a given Domain.

Reimplemented in Kadath::Metric_nophi_AADS, Kadath::Metric_nophi, Kadath::Metric_flat_nophi, Kadath::Metric_cfc, Kadath::Metric_conf_factor, Kadath::Metric_conf, Kadath::Metric_general, and Kadath::Metric_flat.

Definition at line 118 of file metric.cpp.

References Kadath::Metric::compute_cov(), and Kadath::Metric::p_met_cov.

◆ manipulate_ind()

void Kadath::Metric_AADS::manipulate_ind	(	Term_eq &	so,
		int	ind
	)		const

virtual

Uses the Metric to manipulate one of the index of a Term_eq (i.e.

moves the index up or down)

Parameters

so	: the `Term_eq` to be manipulated.
ind	: index number.

Reimplemented from Kadath::Metric.

Definition at line 223 of file metric_AADS.cpp.

References Kadath::Index::inc(), Kadath::Tensor::set(), Kadath::Array< T >::set(), Kadath::Index::set(), Kadath::Scalar::set_domain(), Kadath::Tensor::set_name_affected(), and Kadath::Tensor::set_name_ind().

◆ set_system() [1/3]

void Kadath::Metric_AADS::set_system	(	System_of_eqs &	syst,
		const char *	name_met,
		const char *	name_hmet
	)

Associates the metric to a given system of equations.

Parameters

syst	: the `System_of_eqs`.
name_met	: name by which the metric will be known in the system (like "g", "f"...)
name_hmet	: name of $h_{ij}$ , difference with the background.

Definition at line 562 of file metric_AADS.cpp.

References Kadath::System_of_eqs::add_var(), m_place_syst, Kadath::System_of_eqs::met, Kadath::System_of_eqs::name_met, Kadath::System_of_eqs::ndom, Kadath::System_of_eqs::nvar, p_hmet, and Kadath::Metric::syst.

◆ set_system() [2/3]

void Kadath::Metric_AADS::set_system	(	System_of_eqs &	syst,
		const char *	name_met,
		const char *	name_hmet,
		const char *	name_back_cov,
		const char *	name_back_con,
		const char *	name_back_gam,
		const char *	name_back_ricci
	)

Associates the metric to a given system of equations.

It also sets the background quantities as constants.

Parameters

syst	: the `System_of_eqs`.
name_met	: name by which the metric will be known in the system (like "g", "f"...)
name_hmet	: name of $h_{ij}$ , difference with the background.
name_back_cov	: name of the convariant background metric
name_back_con	: name of the contravariant background metric.
name_back_gam	: name of the background Christoffels.
name_back_ricci	: name of the backgroundRicci tensor.

Definition at line 593 of file metric_AADS.cpp.

References Kadath::System_of_eqs::add_var(), Kadath::Metric_ADS::init_system(), m_ads, m_place_syst, Kadath::System_of_eqs::met, Kadath::System_of_eqs::name_met, Kadath::System_of_eqs::ndom, Kadath::System_of_eqs::nvar, p_hmet, and Kadath::Metric::syst.

◆ set_system() [3/3]

void Kadath::Metric_AADS::set_system	(	System_of_eqs &	syst,
		const char *	name_met,
		const char *	name_hmet,
		const char *	name_back_cov,
		const char *	name_back_con,
		const char *	name_back_ricci
	)

Associates the metric to a given system of equations.

It also sets the background quantities as constants.

Parameters

syst	: the `System_of_eqs`.
name_met	: name by which the metric will be known in the system (like "g", "f"...)
name_hmet	: name of $h_{ij}$ , difference with the background.
name_back_cov	: name of the background convariant metric
name_back_con	: name of the background contravariant description.
name_back_ricci	: name of the background Ricci tensor.

Definition at line 577 of file metric_AADS.cpp.

References Kadath::System_of_eqs::add_var(), Kadath::Metric_ADS::init_system(), m_ads, m_place_syst, Kadath::System_of_eqs::met, Kadath::System_of_eqs::name_met, Kadath::System_of_eqs::ndom, Kadath::System_of_eqs::nvar, p_hmet, and Kadath::Metric::syst.

◆ update() [1/2]

void Kadath::Metric_AADS::update ( )

protectedvirtual

Updates the derived quantities (Christoffels etc..) This is done only for the ones that are needed, i.e.

for the ones that have already been computed.

Reimplemented from Kadath::Metric.

Definition at line 87 of file metric_AADS.cpp.

References m_nd.

◆ update() [2/2]

void Kadath::Metric_AADS::update ( int dd )

protectedvirtual

Updates the derived quantities (Christoffels etc..) in a given Domain This is done only for the ones that are needed, i.e.

for the ones that have already been computed.

Parameters

dd	: the index of the `Domain`.

Reimplemented from Kadath::Metric.

Definition at line 77 of file metric_AADS.cpp.

References compute_christo(), compute_con(), compute_cov(), compute_ricci_scalar(), compute_ricci_tensor(), Kadath::Metric::p_christo, Kadath::Metric::p_met_con, Kadath::Metric::p_met_cov, Kadath::Metric::p_ricci_scalar, Kadath::Metric::p_ricci_tensor, and Kadath::Metric::type_tensor.

Member Data Documentation

◆ espace

const Space& Kadath::Metric::espace

protectedinherited

The associated Space.

Definition at line 42 of file metric.hpp.

◆ m_ads

Metric_ADS Kadath::Metric_AADS::m_ads

protected

Background metric(i.e. ADS metric).

Definition at line 135 of file metric_AADS.hpp.

◆ m_doder

bool Kadath::Metric_AADS::m_doder

mutableprotected

true if metric variation allowed to be computed

Definition at line 134 of file metric_AADS.hpp.

◆ m_L

double Kadath::Metric_AADS::m_L

protected

AdS length.

Definition at line 133 of file metric_AADS.hpp.

◆ m_nd

int Kadath::Metric_AADS::m_nd

protected

number of physical domains (usually the last compaxtified domain is discarded).

Definition at line 131 of file metric_AADS.hpp.

◆ m_place_syst

int Kadath::Metric_AADS::m_place_syst

protected

Where is the unknown h in the system of equations.

Definition at line 132 of file metric_AADS.hpp.

◆ p_basis

Base_tensor* Kadath::Metric_AADS::p_basis

protected

Pointer on the tensorial basis (Cartesian basis only).

Definition at line 138 of file metric_AADS.hpp.

◆ p_christo

MMPtr_array<Term_eq> Kadath::Metric::p_christo

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the Christoffel symbols, in a given Domain.

Definition at line 60 of file metric.hpp.

◆ p_der_eps

Vector* Kadath::Metric_AADS::p_der_eps

protected

Pointer on the vector containing the derivative of the conformal factor $D_i \epsilon$ .

Definition at line 137 of file metric_AADS.hpp.

◆ p_det_cov

MMPtr_array<Term_eq> Kadath::Metric::p_det_cov

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto determinant of the covariant representation, in a given Domain.

Definition at line 85 of file metric.hpp.

◆ p_dirac

MMPtr_array<Term_eq> Kadath::Metric::p_dirac

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto the potential of the Dirac gauge, in a given Domain.

Definition at line 80 of file metric.hpp.

◆ p_h

Term_eq** Kadath::Metric_AADS::p_h

mutableprivate

Pointers on the differences between the covariant metric and the covariant background.

Definition at line 141 of file metric_AADS.hpp.

◆ p_hmet

Metric_tensor* Kadath::Metric_AADS::p_hmet

protected

$h_{ij}$ : the discrepancy between covariant metric and contravariant background.

Definition at line 136 of file metric_AADS.hpp.

◆ p_k

Term_eq** Kadath::Metric_AADS::p_k

mutableprivate

Pointers on the differences between the contravariant metric and the contravariant background.

Definition at line 142 of file metric_AADS.hpp.

◆ p_met_con

MMPtr_array<Term_eq> Kadath::Metric::p_met_con

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the contravariant representation of the Metric, in a given Domain.

Definition at line 55 of file metric.hpp.

◆ p_met_cov

MMPtr_array<Term_eq> Kadath::Metric::p_met_cov

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the covariant representation of the Metric, in a given Domain.

Definition at line 50 of file metric.hpp.

◆ p_ricci_scalar

MMPtr_array<Term_eq> Kadath::Metric::p_ricci_scalar

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto the Ricci scalar, in a given Domain.

Definition at line 75 of file metric.hpp.

◆ p_ricci_tensor

MMPtr_array<Term_eq> Kadath::Metric::p_ricci_tensor

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the Ricci tensor, in a given Domain.

Definition at line 70 of file metric.hpp.

◆ p_riemann

MMPtr_array<Term_eq> Kadath::Metric::p_riemann

mutableprotectedinherited

Array of pointers on various Term_eq.

Each one points onto one component of the Riemann tensor, in a given Domain.

Definition at line 65 of file metric.hpp.

◆ syst

const System_of_eqs* Kadath::Metric::syst

protectedinherited

Pointer of the system of equations where the metric is used (only one for now).

Definition at line 44 of file metric.hpp.

◆ type_tensor

int Kadath::Metric::type_tensor

protectedinherited

States if one works in the CON or COV representation.

Definition at line 86 of file metric.hpp.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Metric_AADS() [1/2]

◆ Metric_AADS() [2/2]

Member Function Documentation

◆ compute_christo()

◆ compute_con()

◆ compute_cov()

◆ compute_det_cov()

◆ compute_dirac()

◆ compute_ricci_scalar()

◆ compute_ricci_tensor()

◆ compute_riemann()

◆ derive()

◆ derive_flat()

◆ derive_partial()

◆ derive_simple()

◆ get_background()

◆ give_christo()

◆ give_det_cov()

◆ give_dirac()

◆ give_ricci_scalar()

◆ give_ricci_tensor()

◆ give_riemann()

◆ give_term()

◆ give_type()

◆ manipulate_ind()

◆ set_system() [1/3]

◆ set_system() [2/3]

◆ set_system() [3/3]

◆ update() [1/2]

◆ update() [2/2]

Member Data Documentation

◆ espace

◆ m_ads

◆ m_doder

◆ m_L

◆ m_nd

◆ m_place_syst

◆ p_basis

◆ p_christo

◆ p_der_eps

◆ p_det_cov

◆ p_dirac

◆ p_h

◆ p_hmet

◆ p_k

◆ p_met_con

◆ p_met_cov

◆ p_ricci_scalar

◆ p_ricci_tensor

◆ p_riemann

◆ syst

◆ type_tensor