Ricci Module

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

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

Bases: BaseRelativityTensor

Class for defining Ricci 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 or None) – Corresponding Metric for the Ricci Tensor. Defaults to None.

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

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_riemann(riemann, parent_metric=None)[source]

Get Ricci Tensor calculated from Riemann Tensor

Parameters:
  • riemann (RiemannCurvatureTensor) – Riemann Tensor

  • parent_metric (MetricTensor or None) – Corresponding Metric for the Ricci Tensor. None if it should inherit the Parent Metric of Riemann Tensor. Defaults to None.

classmethod from_christoffels(chris, parent_metric=None)[source]

Get Ricci Tensor calculated from Christoffel Tensor

Parameters:
  • chris (ChristoffelSymbols) – Christoffel Tensor

  • parent_metric (MetricTensor or None) – Corresponding Metric for the Ricci Tensor. None if it should inherit the Parent Metric of Christoffel Symbols. Defaults to None.

classmethod from_metric(metric)[source]

Get Ricci Tensor calculated from Metric Tensor

Parameters:

metric (MetricTensor) – Metric Tensor

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 somehow does not have a parent metric. Defaults to None.

Returns:

New tensor with new configuration. Defaults to ‘ul’

Return type:

RicciTensor

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:

RicciTensor

class einsteinpy.symbolic.ricci.RicciScalar(arr, syms, parent_metric=None)[source]

Bases: BaseRelativityTensor

Class for defining Ricci Scalar

Constructor and Initializer

Parameters:
  • arr (ImmutableDenseNDimArray or list) – Sympy Array, multi-dimensional list containing Sympy Expressions, or Sympy Expressions or int or float scalar

  • syms (tuple or list) – Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3)

  • parent_metric (MetricTensor or None) – Corresponding Metric for the Ricci Scalar. Defaults to None.

Raises:

TypeError – Raised when syms is not a list or tuple

property expr

Retuns the symbolic expression of the Ricci Scalar

classmethod from_riccitensor(riccitensor, parent_metric=None)[source]

Get Ricci Scalar calculated from Ricci Tensor

Parameters:
  • riccitensor (RicciTensor) – Ricci Tensor

  • parent_metric (MetricTensor or None) – Corresponding Metric for the Ricci Scalar. Defaults to None.

classmethod from_riemann(riemann, parent_metric=None)[source]

Get Ricci Scalar calculated from Riemann Tensor

Parameters:
classmethod from_christoffels(chris, parent_metric=None)[source]

Get Ricci Scalar calculated from Christoffel Tensor

Parameters:
  • chris (ChristoffelSymbols) – Christoffel Tensor

  • parent_metric (MetricTensor or None) – Corresponding Metric for the Ricci Scalar. Defaults to None.

classmethod from_metric(metric)[source]

Get Ricci Scalar calculated from Metric Tensor

Parameters:

metric (MetricTensor) – Metric Tensor