Christoffel Symbols Module¶
This module contains the class for obtaining Christoffel Symbols related to a Metric belonging to any arbitrary space-time symbolically:
-
class
einsteinpy.symbolic.christoffel.
ChristoffelSymbols
(arr, syms, config='ull', parent_metric=None, name='ChristoffelSymbols')[source]¶ Bases:
einsteinpy.symbolic.tensor.BaseRelativityTensor
Class for defining christoffel symbols.
Constructor and Initializer
- Parameters
arr (ImmutableDenseNDimArray or list) – Sympy Array or multi-dimensional list containing Sympy Expressions
syms (tuple or list) – Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3)
config (str) – Configuration of contravariant and covariant indices in tensor. ‘u’ for upper and ‘l’ for lower indices. Defaults to ‘ull’.
parent_metric (MetricTensor) – Metric Tensor from which Christoffel symbol is calculated. Defaults to None.
name (str) – Name of the Christoffel Symbols Tensor. Defaults to “ChristoffelSymbols”.
- Raises
TypeError – Raised when arr is not a list or sympy Array
TypeError – syms is not a list or tuple
ValueError – config has more or less than 3 indices
-
classmethod
from_metric
(metric)[source]¶ Get Christoffel symbols calculated from a metric tensor
- Parameters
metric (MetricTensor) – Space-time Metric from which Christoffel Symbols are to be calculated
-
change_config
(newconfig='lll', metric=None)[source]¶ Changes the index configuration(contravariant/covariant)
- Parameters
newconfig (str) – Specify the new configuration. Defaults to ‘lll’
metric (MetricTensor or None) – Parent metric tensor for changing indices. Already assumes the value of the metric tensor from which it was initialized if passed with None. Compulsory if not initialized with ‘from_metric’. Defaults to None.
- Returns
New tensor with new configuration. Defaults to ‘lll’
- Return type
- Raises
Exception – Raised when a parent metric could not be found.