Metric Tensor Module¶
This module contains the class for defining a Metric belonging to any arbitrary space-time symbolically:
-
class
einsteinpy.symbolic.metric.MetricTensor(arr, syms, config='ll')¶ Inherits from ~einsteinpy.symbolic.tensor.BaseRelativityTensor . Class to define a metric tensor for a space-time
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’.
- 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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change_config(newconfig='uu')¶ Changes the index configuration(contravariant/covariant)
- Parameters
newconfig (str) – Specify the new configuration. Defaults to ‘uu’
- Returns
New Metric with new configuration. Defaults to ‘uu’
- Return type
- Raises
ValueError – Raised when new configuration is not ‘ll’ or ‘uu’. This constraint is in place because we are dealing with Metric Tensor.
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inv()¶ Returns the inverse of the Metric. Returns contravariant Metric if it is originally covariant or vice-versa.
- Returns
New Metric which is the inverse of original Metric.
- Return type
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lower_config()¶ Returns a covariant instance of the given metric tensor.
- Returns
same instance if the configuration is already lower or inverse of given metric if configuration is upper
- Return type
