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:
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.
- lorentz_transform(transformation_matrix)[source]¶
Performs a Lorentz transform on the tensor.
- Parameters:
transformation_matrix (ImmutableDenseNDimArray or list) – Sympy Array or multi-dimensional list containing Sympy Expressions
- Returns:
lorentz transformed tensor
- Return type: