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)¶ 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 dentoting 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.
- 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
-
property
parent_metric
¶ Returns the Parent Metric, if available.
-
classmethod
from_christoffels
(chris, parent_metric=None)¶ Get Riemann Tensor calculated from a Christoffel Symbols
- Parameters
chris (ChristoffelSymbols) – Christoffel Symbols from which Riemann Curvature Tensor to be calculated
parent_metric (MetricTensor or None) – Corrosponding Metric for the Riemann Tensor. None if it should inherit the Parent Metric of Christoffel Symbols. Defaults to None.
-
classmethod
from_metric
(metric)¶ Get Riemann Tensor calculated from a Metric Tensor
- Parameters
metric (MetricTensor) – Metric Tensor from which Riemann Curvature Tensor to be calculated
-
change_config
(newconfig='llll', metric=None)¶ 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.