Source code for einsteinpy.symbolic.schouten
from einsteinpy.symbolic.helpers import _change_name
from einsteinpy.symbolic.ricci import RicciScalar, RicciTensor
from einsteinpy.symbolic.riemann import RiemannCurvatureTensor
from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config
[docs]
class SchoutenTensor(BaseRelativityTensor):
"""
Class for defining Schouten Tensor
"""
def __init__(
self, arr, syms, config="ll", parent_metric=None, name="SchoutenTensor"
):
"""
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'.
parent_metric : ~einsteinpy.symbolic.metric.MetricTensor
Corresponding Metric for the Schouten Tensor. Defaults to None.
name : str
Name of the Tensor. Defaults to "SchoutenTensor".
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(SchoutenTensor, self).__init__(
arr=arr, syms=syms, config=config, parent_metric=parent_metric, name=name
)
self._order = 2
if not len(config) == self._order:
raise ValueError("config should be of length {}".format(self._order))
[docs]
@classmethod
def from_metric(cls, metric):
"""
Get Schouten tensor calculated from a metric tensor
Parameters
----------
metric : ~einsteinpy.symbolic.metric.MetricTensor
Space-time Metric from which Christoffel Symbols are to be calculated
Raises
------
ValueError
Raised when the dimension of the tensor is less than 3
"""
if metric.dims >= 3:
t_ricci = RicciTensor.from_metric(metric)
r_scalar = RicciScalar.from_riccitensor(t_ricci, parent_metric=None)
dims = metric.dims
t_schouten = (
t_ricci.tensor()
- (r_scalar.expr * metric.lower_config().tensor() / (2 * (dims - 1)))
) / (dims - 2)
return cls(t_schouten, metric.syms, config="ll", parent_metric=metric)
raise ValueError("Dimension of the space/space-time should be 3 or more")
[docs]
def change_config(self, newconfig="ul", metric=None):
"""
Changes the index configuration(contravariant/covariant)
Parameters
----------
newconfig : str
Specify the new configuration. Defaults to 'ul'
metric : ~einsteinpy.symbolic.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
-------
~einsteinpy.symbolic.schouten.SchoutenTensor
New tensor with new configuration. Configuration defaults to 'ul'
Raises
------
Exception
Raised when a parent metric could not be found.
"""
if metric is None:
metric = self._parent_metric
if metric is None:
raise Exception("Parent Metric not found, can't do configuration change")
new_tensor = _change_config(self, metric, newconfig)
new_obj = SchoutenTensor(
new_tensor,
self.syms,
config=newconfig,
parent_metric=metric,
name=_change_name(self.name, context="__" + newconfig),
)
return new_obj
