Riemann Tensor Module¶
This module contains the class for obtaining Riemann Curvature Tensor related to a Metric belonging to any arbitrary space-time symbolically:
-
class
einsteinpy.symbolic.riemann.
RiemannCurvatureTensor
(arr, syms, config='ulll', parent_metric=None, name='RiemannCurvatureTensor')[source]¶ Bases:
einsteinpy.symbolic.tensor.BaseRelativityTensor
Class for defining Riemann Curvature 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 ‘ulll’.
parent_metric (MetricTensor) – Metric Tensor related to this Riemann Curvature Tensor.
name (str) – Name of the Tensor. Defaults to “RiemannCurvatureTensor”.
- 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 4 indices
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classmethod
from_christoffels
(chris, parent_metric=None)[source]¶ Get Riemann Tensor calculated from Christoffel Symbols. Reimann Tensor is given as:
\[R^{t}{}_{s r n}=\Gamma^{t}{}_{s n, r} - \Gamma^{t }{}_{s r, n } + \Gamma^{p}{}_{s n}\Gamma^{t}{}_{p r} - \Gamma^{p}{}_{s r}\Gamma^{t}{}_{p n}\]- Parameters
chris (ChristoffelSymbols) – Christoffel Symbols from which Riemann Curvature Tensor to be calculated
parent_metric (MetricTensor or None) – Corresponding Metric for the Riemann Tensor. None if it should inherit the Parent Metric of Christoffel Symbols. Defaults to None.
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classmethod
from_metric
(metric)[source]¶ Get Riemann Tensor calculated from a Metric Tensor
- Parameters
metric (MetricTensor) – Metric Tensor from which Riemann Curvature Tensor to be calculated
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change_config
(newconfig='llll', metric=None)[source]¶ Changes the index configuration(contravariant/covariant)
- Parameters
newconfig (str) – Specify the new configuration. Defaults to ‘llll’
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 ‘llll’
- Return type
- Raises
Exception – Raised when a parent metric could not be found.