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:

ChristoffelSymbols

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:

ChristoffelSymbols