import sympy
from sympy import tensorcontraction, tensorproduct
from einsteinpy.symbolic.christoffel import ChristoffelSymbols
from einsteinpy.symbolic.helpers import _change_name, simplify_sympy_array
from einsteinpy.symbolic.metric import MetricTensor
from einsteinpy.symbolic.riemann import RiemannCurvatureTensor
from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config
[docs]
class RicciTensor(BaseRelativityTensor):
"""
Class for defining Ricci Tensor
"""
def __init__(self, arr, syms, config="ll", parent_metric=None, name="RicciTensor"):
"""
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 or None
Corresponding Metric for the Ricci Tensor.
Defaults to None.
name : str
Name of the Tensor. Defaults to "RicciTensor".
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(RicciTensor, 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_riemann(cls, riemann, parent_metric=None):
"""
Get Ricci Tensor calculated from Riemann Tensor
Parameters
----------
riemann : ~einsteinpy.symbolic.riemann.RiemannCurvatureTensor
Riemann Tensor
parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None
Corresponding Metric for the Ricci Tensor.
None if it should inherit the Parent Metric of Riemann Tensor.
Defaults to None.
"""
if not riemann.config == "ulll":
riemann = riemann.change_config(newconfig="ulll", metric=parent_metric)
if parent_metric is None:
parent_metric = riemann.parent_metric
return cls(
simplify_sympy_array(sympy.tensorcontraction(riemann.tensor(), (0, 2))),
riemann.syms,
config="ll",
parent_metric=parent_metric,
)
[docs]
@classmethod
def from_christoffels(cls, chris, parent_metric=None):
"""
Get Ricci Tensor calculated from Christoffel Tensor
Parameters
----------
chris : ~einsteinpy.symbolic.christoffel.ChristoffelSymbols
Christoffel Tensor
parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None
Corresponding Metric for the Ricci Tensor.
None if it should inherit the Parent Metric of Christoffel Symbols.
Defaults to None.
"""
rt = RiemannCurvatureTensor.from_christoffels(
chris, parent_metric=parent_metric
)
return cls.from_riemann(rt)
[docs]
@classmethod
def from_metric(cls, metric):
"""
Get Ricci Tensor calculated from Metric Tensor
Parameters
----------
metric : ~einsteinpy.symbolic.metric.MetricTensor
Metric Tensor
"""
ch = ChristoffelSymbols.from_metric(metric)
return cls.from_christoffels(ch, parent_metric=None)
[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 somehow does not have a parent metric. Defaults to None.
Returns
-------
~einsteinpy.symbolic.ricci.RicciTensor
New tensor with new 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 = RicciTensor(
new_tensor,
self.syms,
config=newconfig,
parent_metric=metric,
name=_change_name(self.name, context="__" + newconfig),
)
return new_obj
[docs]
class RicciScalar(BaseRelativityTensor):
"""
Class for defining Ricci Scalar
"""
def __init__(self, arr, syms, parent_metric=None):
"""
Constructor and Initializer
Parameters
----------
arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list
Sympy Array, multi-dimensional list containing Sympy Expressions, or Sympy Expressions or int or float scalar
syms : tuple or list
Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3)
parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None
Corresponding Metric for the Ricci Scalar.
Defaults to None.
Raises
------
TypeError
Raised when syms is not a list or tuple
"""
super(RicciScalar, self).__init__(
arr=arr,
syms=syms,
config="",
parent_metric=parent_metric,
name="RicciScalar",
)
self._order = 0
@property
def expr(self):
"""
Retuns the symbolic expression of the Ricci Scalar
"""
val = sum(self.arr) # sympy not allowing indexing, temporary fix!
return val
[docs]
@classmethod
def from_riccitensor(cls, riccitensor, parent_metric=None):
"""
Get Ricci Scalar calculated from Ricci Tensor
Parameters
----------
riccitensor: ~einsteinpy.symbolic.metric.RicciTensor
Ricci Tensor
parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None
Corresponding Metric for the Ricci Scalar.
Defaults to None.
"""
if not riccitensor.config == "ul":
riccitensor = riccitensor.change_config(
newconfig="ul", metric=parent_metric
)
if parent_metric is None:
parent_metric = riccitensor.parent_metric
ricci_scalar = tensorcontraction(riccitensor.tensor(), (0, 1))
return cls(
simplify_sympy_array(ricci_scalar),
riccitensor.syms,
parent_metric=parent_metric,
)
[docs]
@classmethod
def from_riemann(cls, riemann, parent_metric=None):
"""
Get Ricci Scalar calculated from Riemann Tensor
Parameters
----------
riemann : ~einsteinpy.symbolic.riemann.RiemannCurvatureTensor
Riemann Tensor
parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None
Corresponding Metric for the Ricci Scalar.
Defaults to None.
"""
cg = RicciTensor.from_riemann(riemann, parent_metric=parent_metric)
return cls.from_riccitensor(cg)
[docs]
@classmethod
def from_christoffels(cls, chris, parent_metric=None):
"""
Get Ricci Scalar calculated from Christoffel Tensor
Parameters
----------
chris : ~einsteinpy.symbolic.christoffel.ChristoffelSymbols
Christoffel Tensor
parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None
Corresponding Metric for the Ricci Scalar.
Defaults to None.
"""
rt = RiemannCurvatureTensor.from_christoffels(
chris, parent_metric=parent_metric
)
return cls.from_riemann(rt)
[docs]
@classmethod
def from_metric(cls, metric):
"""
Get Ricci Scalar calculated from Metric Tensor
Parameters
----------
metric : ~einsteinpy.symbolic.metric.MetricTensor
Metric Tensor
"""
ch = ChristoffelSymbols.from_metric(metric)
return cls.from_christoffels(ch, parent_metric=None)
