Christoffel Symbols Module¶
This module contains the class for obtaining Christoffel Symbols related to a Metric belonging to any arbitrary space-time symbolically:
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class
einsteinpy.symbolic.christoffel.
ChristoffelSymbols
(arr, syms, config='ull', parent_metric=None)¶ Class for defining christoffel symbols
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 ‘ull’.
- parent_metric (MetricTensor) – Metric Tensor from which Christoffel symbol is calculated. Defaults to None.
Raises: TypeError
– Raised when arr is not a list or sympy ArrayTypeError
– syms is not a list or tupleValueError
– config has more or less than 3 indices
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parent_metric
¶ Returns the Metric from which Christoffel Symbol was derived, if available.
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classmethod
from_metric
(metric)¶ Get Christoffel symbols calculated from a metric tensor
Parameters: metric (MetricTensor) – Space-time Metric from which Christoffel Symbols are to be calculated
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change_config
(newconfig='lll', metric=None)¶ Changes the index configuration(contravariant/covariant)
Parameters: - newconfig (str) – Specify the new configuration. Defaults to ‘lll’
- 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. Defaults to ‘lll’
Return type: Raises: Exception
– Raised when a parent metric could not be found.