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')¶ 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 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 ‘ll’.
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 2 indices
-
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: MetricTensor Raises: ValueError
– Raised when new configuration is not ‘ll’ or ‘uu’. This constraint is in place because we are dealing with Metric Tensor.
-
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: MetricTensor