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(, 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()
[docs] def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.metric.MetricTensor lorentz transformed tensor """ t = super(MetricTensor, self).lorentz_transform(transformation_matrix) return MetricTensor( t.tensor(), syms=self.syms, config=self._config, name=_change_name(, context="__lt"), )