LORENE

Class Connection_flat. More...
#include <connection.h>
Public Member Functions  
Connection_flat (const Connection_flat &)  
Copy constructor. More...  
virtual  ~Connection_flat () 
destructor More...  
void  operator= (const Connection_flat &) 
Assignment to another Connection_flat . More...  
virtual Tensor *  p_derive_cov (const Tensor &tens) const =0 
Computes the covariant derivative of a tensor (with respect to the current connection). More...  
virtual Tensor *  p_divergence (const Tensor &tens) const =0 
Computes the divergence of a tensor (with respect to the current connection). More...  
virtual const Tensor &  ricci () const 
Computes (if not up to date) and returns the Ricci tensor associated with the current connection. More...  
void  update (const Tensor_sym &delta_i) 
Update the connection when it is defined ab initio. More...  
void  update (const Metric &met) 
Update the connection when it is associated with a metric. More...  
const Map &  get_mp () const 
Returns the mapping. More...  
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. More...  
Protected Member Functions  
Connection_flat (const Map &, const Base_vect &)  
Contructor from a triad, has to be defined in the derived classes. More...  
void  del_deriv () const 
Deletes all the derived quantities. More...  
void  set_der_0x0 () const 
Sets to 0x0 all the pointers on derived quantities. More...  
Protected Attributes  
const Map *const  mp 
Reference mapping. More...  
const Base_vect *const  triad 
Triad with respect to which the connection coefficients are defined. More...  
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. More...  
bool  assoc_metric 
Indicates whether the connection is associated with a metric (in which case the Ricci tensor is symmetric, i.e. More...  
Tensor *  p_ricci 
Pointer of the Ricci tensor associated with the connection. More...  
Class Connection_flat.
()
Abstract class for connections associated with a flat metric.
Definition at line 354 of file connection.h.
Contructor from a triad, has to be defined in the derived classes.
Definition at line 80 of file connection_flat.C.
References Lorene::Connection::assoc_metric, Lorene::Connection::delta, and Lorene::Tensor::set_etat_zero().
Lorene::Connection_flat::Connection_flat  (  const Connection_flat &  ci  ) 
Copy constructor.
Definition at line 90 of file connection_flat.C.

virtual 
destructor
Definition at line 100 of file connection_flat.C.

protectedinherited 
Deletes all the derived quantities.
Definition at line 208 of file connection.C.
References Lorene::Connection::p_ricci, and Lorene::Connection::set_der_0x0().

inlineinherited 
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.

inlineinherited 
Returns the mapping.
Definition at line 253 of file connection.h.
References Lorene::Connection::mp.
void Lorene::Connection_flat::operator=  (  const Connection_flat &  ) 
Assignment to another Connection_flat
.
Definition at line 110 of file connection_flat.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 1form, 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. Reimplemented from Lorene::Connection.
Implemented in Lorene::Connection_fcart, and Lorene::Connection_fspher.
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. Reimplemented from Lorene::Connection.
Implemented in Lorene::Connection_fcart, and Lorene::Connection_fspher.

virtual 
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.

protectedinherited 
Sets to 0x0
all the pointers on derived quantities.
Definition at line 216 of file connection.C.
References Lorene::Connection::p_ricci.

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().

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.

protectedinherited 
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.

protectedinherited 
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.

protectedinherited 
Reference mapping.
Definition at line 119 of file connection.h.

mutableprotectedinherited 
Pointer of the Ricci tensor associated with the connection.
Definition at line 164 of file connection.h.

protectedinherited 
Triad with respect to which the connection coefficients are defined.
Definition at line 124 of file connection.h.