LORENE
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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.
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virtual |
destructor
Definition at line 100 of file connection_flat.C.
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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().
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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.
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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 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. 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.
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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.
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protectedinherited |
Sets to 0x0
all the pointers on derived quantities.
Definition at line 216 of file connection.C.
References Lorene::Connection::p_ricci.
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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().
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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.
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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.
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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.
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protectedinherited |
Reference mapping.
Definition at line 119 of file connection.h.
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mutableprotectedinherited |
Pointer of the Ricci tensor associated with the connection.
Definition at line 164 of file connection.h.
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protectedinherited |
Triad with respect to which the connection coefficients are defined.
Definition at line 124 of file connection.h.