Class Connection_fspher. More...
#include <connection.h>
Public Member Functions | |
Connection_fspher (const Map &, const Base_vect_spher &) | |
Contructor from a spherical flat-metric-orthonormal basis. | |
Connection_fspher (const Connection_fspher &) | |
Copy constructor. | |
virtual | ~Connection_fspher () |
destructor | |
void | operator= (const Connection_fspher &) |
Assignment to another Connection_fspher . | |
virtual Tensor * | p_derive_cov (const Tensor &tens) const |
Computes the covariant derivative of a tensor (with respect to the current connection). | |
virtual Tensor * | p_divergence (const Tensor &tens) const |
Computes the divergence of a tensor (with respect to the current connection). | |
virtual const Tensor & | ricci () const |
Computes (if not up to date) and returns the Ricci tensor associated with the current connection. | |
void | update (const Tensor_sym &delta_i) |
Update the connection when it is defined ab initio. | |
void | update (const Metric &met) |
Update the connection when it is associated with a metric. | |
const Map & | get_mp () const |
Returns the mapping. | |
const Tensor_sym & | get_delta () const |
Returns the tensor which defines the connection with respect to the flat one: is the difference between the connection coefficients and the connection coefficients of the flat connection. | |
Protected Member Functions | |
void | del_deriv () const |
Deletes all the derived quantities. | |
void | set_der_0x0 () const |
Sets to 0x0 all the pointers on derived quantities. | |
Protected Attributes | |
const Map *const | mp |
Reference mapping. | |
const Base_vect *const | triad |
Triad with respect to which the connection coefficients are defined. | |
Tensor_sym | delta |
Tensor which defines the connection with respect to the flat one: is the difference between the connection coefficients and the connection coefficients of the flat connection. | |
bool | assoc_metric |
Indicates whether the connection is associated with a metric (in which case the Ricci tensor is symmetric, i.e. | |
Tensor * | p_ricci |
Pointer of the Ricci tensor associated with the connection. |
Class Connection_fspher.
()
Class for connections associated with a flat metric and given onto an orthonormal spherical triad.
Definition at line 452 of file connection.h.
Lorene::Connection_fspher::Connection_fspher | ( | const Map & | mpi, | |
const Base_vect_spher & | bi | |||
) |
Contructor from a spherical flat-metric-orthonormal basis.
Definition at line 145 of file connection_fspher.C.
Lorene::Connection_fspher::Connection_fspher | ( | const Connection_fspher & | ci | ) |
Copy constructor.
Definition at line 151 of file connection_fspher.C.
Lorene::Connection_fspher::~Connection_fspher | ( | ) | [virtual] |
destructor
Definition at line 161 of file connection_fspher.C.
void Lorene::Connection::del_deriv | ( | ) | const [protected, inherited] |
Deletes all the derived quantities.
Definition at line 208 of file connection.C.
References Lorene::Connection::p_ricci, and Lorene::Connection::set_der_0x0().
const Tensor_sym& Lorene::Connection::get_delta | ( | ) | const [inline, inherited] |
Returns the tensor which defines the connection with respect to the flat one: is the difference between the connection coefficients and the connection coefficients of the flat connection.
The connection coefficients with respect to the triad are defined according to the MTW convention:
Note that is symmetric with respect to the indices j and k.
delta}
(i,j,k) = Definition at line 271 of file connection.h.
References Lorene::Connection::delta.
const Map& Lorene::Connection::get_mp | ( | ) | const [inline, inherited] |
Returns the mapping.
Definition at line 253 of file connection.h.
References Lorene::Connection::mp.
void Lorene::Connection_fspher::operator= | ( | const Connection_fspher & | ) |
Assignment to another Connection_fspher
.
Reimplemented from Lorene::Connection_flat.
Definition at line 171 of file connection_fspher.C.
Computes the covariant derivative of a tensor (with respect to the current connection).
The extra index (with respect to the indices of ) of is chosen to be the last one. This convention agrees with that of MTW (see Eq. (10.17) of MTW). For instance, if is a 1-form, whose components w.r.t. the triad are : , then the covariant derivative of is the bilinear form whose components are such that
tens | tensor |
Vector
if the argument is a Scalar
, and on a Tensor
otherwise. NB: The corresponding memory is allocated by the method p_derive_cov()
and must be deallocated by the user afterwards. Implements Lorene::Connection_flat.
Definition at line 186 of file connection_fspher.C.
References Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::div_tant(), Lorene::Tensor::get_index_type(), Lorene::Map::get_mg(), Lorene::Tensor::get_n_comp(), Lorene::Mg3d::get_nzone(), Lorene::Tensor::get_triad(), Lorene::Mg3d::get_type_r(), Lorene::Tensor::get_valence(), Lorene::Tensor::indices(), Lorene::Connection::mp, Lorene::Tensor::set(), Lorene::Itbl::set(), Lorene::Tensor_sym::sym_index1(), Lorene::Tensor_sym::sym_index2(), and Lorene::Connection::triad.
Computes the divergence of a tensor (with respect to the current connection).
The divergence is taken with respect of the last index of which thus must be contravariant. For instance if is a twice contravariant tensor, whose components w.r.t. the triad are : , the divergence of is the vector
where denotes the current connection.
tens | tensor |
Scalar
if is a Vector
, on a Vector
if is a tensor of valence 2, and on a Tensor
otherwise. NB: The corresponding memory is allocated by the method p_divergence()
and must be deallocated by the user afterwards. Implements Lorene::Connection_flat.
Definition at line 434 of file connection_fspher.C.
References Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::div_tant(), Lorene::Tensor::get_index_type(), Lorene::Tensor::get_n_comp(), Lorene::Tensor::get_triad(), Lorene::Tensor::get_valence(), Lorene::Tensor::indices(), Lorene::Connection::mp, Lorene::Itbl::set(), Lorene::Tensor_sym::sym_index1(), Lorene::Tensor_sym::sym_index2(), and Lorene::Connection::triad.
const Tensor & Lorene::Connection_flat::ricci | ( | ) | const [virtual, inherited] |
Computes (if not up to date) and returns the Ricci tensor associated with the current connection.
Reimplemented from Lorene::Connection.
Definition at line 124 of file connection_flat.C.
References Lorene::Connection::mp, Lorene::Connection::p_ricci, Lorene::Tensor::set_etat_zero(), and Lorene::Connection::triad.
void Lorene::Connection::set_der_0x0 | ( | ) | const [protected, inherited] |
Sets to 0x0
all the pointers on derived quantities.
Definition at line 216 of file connection.C.
References Lorene::Connection::p_ricci.
void Lorene::Connection::update | ( | const Metric & | met | ) | [inherited] |
Update the connection when it is associated with a metric.
met | Metric to which the connection is associated |
Definition at line 258 of file connection.C.
References Lorene::Connection::assoc_metric, Lorene::Connection::del_deriv(), Lorene::Connection::fait_delta(), and Lorene::Connection::flat_met.
void Lorene::Connection::update | ( | const Tensor_sym & | delta_i | ) | [inherited] |
Update the connection when it is defined ab initio.
delta_i | tensor which defines the connection with respect to the flat one: is the difference between the connection coefficients and the connection coefficients of the flat connection. must be symmetric with respect to the indices j and k. |
Definition at line 238 of file connection.C.
References Lorene::Connection::assoc_metric, Lorene::Connection::del_deriv(), Lorene::Connection::delta, Lorene::Connection::flat_met, Lorene::Tensor::get_index_type(), Lorene::Tensor::get_valence(), Lorene::Tensor_sym::sym_index1(), and Lorene::Tensor_sym::sym_index2().
bool Lorene::Connection::assoc_metric [protected, inherited] |
Indicates whether the connection is associated with a metric (in which case the Ricci tensor is symmetric, i.e.
the actual type of p_ricci
is a Sym_tensor
)
Definition at line 147 of file connection.h.
Tensor_sym Lorene::Connection::delta [protected, inherited] |
Tensor which defines the connection with respect to the flat one: is the difference between the connection coefficients and the connection coefficients of the flat connection.
The connection coefficients with respect to the triad are defined according to the MTW convention:
Note that is symmetric with respect to the indices j and k.
Definition at line 141 of file connection.h.
const Map* const Lorene::Connection::mp [protected, inherited] |
Reference mapping.
Definition at line 119 of file connection.h.
Tensor* Lorene::Connection::p_ricci [mutable, protected, inherited] |
Pointer of the Ricci tensor associated with the connection.
Definition at line 164 of file connection.h.
const Base_vect* const Lorene::Connection::triad [protected, inherited] |
Triad with respect to which the connection coefficients are defined.
Definition at line 124 of file connection.h.