Source code for einsteinpy.symbolic.metric
import sympy
from einsteinpy.symbolic.helpers import _change_name
from einsteinpy.symbolic.tensor import BaseRelativityTensor
[docs]class MetricTensor(BaseRelativityTensor):
"""
Class to define a metric tensor for a space-time
"""
def __init__(self, arr, syms, config="ll", name="GenericMetricTensor"):
"""
Constructor and Initializer
Parameters
----------
arr : ~sympy.tensor.array.dense_ndim_array.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
"""
super(MetricTensor, self).__init__(
arr=arr, syms=syms, config=config, parent_metric=self, name=name
)
self._order = 2
self._invmetric = None
if not len(config) == self._order:
raise ValueError("config should be of length {}".format(self._order))
[docs] def change_config(self, newconfig="uu"):
"""
Changes the index configuration(contravariant/covariant)
Parameters
----------
newconfig : str
Specify the new configuration. Defaults to 'uu'
Returns
-------
~einsteinpy.symbolic.metric.MetricTensor
New Metric with new configuration. Defaults to 'uu'
Raises
------
ValueError
Raised when new configuration is not 'll' or 'uu'.
This constraint is in place because we are dealing with Metric Tensor.
"""
if newconfig == self.config:
return self
if newconfig == "uu" or newconfig == "ll":
inv_met = MetricTensor(
sympy.simplify(sympy.Matrix(self.arr.tolist()).inv()).tolist(),
self.syms,
config=newconfig,
name=_change_name(self.name, context="__" + newconfig),
)
inv_met._invmetric = self
return inv_met
raise ValueError(
"Configuration can't have one upper and one lower index in Metric Tensor."
)
[docs] def inv(self):
"""
Returns the inverse of the Metric.
Returns contravariant Metric if it is originally covariant or vice-versa.
Returns
-------
~einsteinpy.symbolic.metric.MetricTensor
New Metric which is the inverse of original Metric.
"""
if self._invmetric is None:
if self.config == "ll":
self._invmetric = self.change_config("uu")
else:
self._invmetric = self.change_config("ll")
return self._invmetric
[docs] def lower_config(self):
"""
Returns a covariant instance of the given metric tensor.
Returns
-------
~einsteinpy.symbolic.metric.MetricTensor
same instance if the configuration is already lower or
inverse of given metric if configuration is upper
"""
if self.config == "ll":
return self
return self.inv()
