Schouten Module

This module contains the basic classes for obtaining Schouten Tensor related to a Metric belonging to any arbitrary space-time symbolically:

class einsteinpy.symbolic.schouten.SchoutenTensor(arr, syms, config='ll', parent_metric=None, name='SchoutenTensor')[source]

Bases: einsteinpy.symbolic.tensor.BaseRelativityTensor

Class for defining Schouten Tensor

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 ‘ll’.

  • parent_metric (MetricTensor) – Corresponding Metric for the Schouten Tensor. Defaults to None.

  • name (str) – Name of the Tensor. Defaults to “SchoutenTensor”.

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 2 indices

classmethod from_metric(metric)[source]

Get Schouten tensor calculated from a metric tensor

Parameters

metric (MetricTensor) – Space-time Metric from which Christoffel Symbols are to be calculated

Raises

ValueError – Raised when the dimension of the tensor is less than 3

change_config(newconfig='ul', metric=None)[source]

Changes the index configuration(contravariant/covariant)

Parameters
  • newconfig (str) – Specify the new configuration. Defaults to ‘ul’

  • 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. Configuration defaults to ‘ul’

Return type

SchoutenTensor

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

SchoutenTensor