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:
einsteinpy.symbolic.tensor.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
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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.
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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
- Raises
Exception – Raised when a parent metric could not be found.
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class
einsteinpy.symbolic.ricci.
RicciScalar
(arr, syms, parent_metric=None)[source]¶ Bases:
einsteinpy.symbolic.tensor.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
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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
riemann (RiemannCurvatureTensor) – Riemann Tensor
parent_metric (MetricTensor or None) – Corresponding Metric for the Ricci Scalar. Defaults to None.
-
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