Metric Tensor Module¶
This module contains the class for defining a Metric of an arbitrary spacetime, symbolically. Note that, only the coordinate symbols are to
be supplied to the syms
parameter, while arr
takes the metric (as a SymPy array), which may contain several constants. The symbols in
syms
define the basis to perform several operations on the metric, such as symbolic differentiation. Symbols, for the constants in the
metric, should be defined independently and used directly in the specification of arr
. Please check the metric definitions in
einsteinpy.symbolic.predefined
for examples of doing this.
-
class
einsteinpy.symbolic.metric.
MetricTensor
(arr, syms, config='ll', name='GenericMetricTensor')[source]¶ Bases:
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’.
name (str) – Name of the Metric Tensor. Defaults to “GenericMetricTensor”.
- 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
-
change_config
(newconfig='uu')[source]¶ 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.
-
inv
()[source]¶ 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
-
lower_config
()[source]¶ 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