Geodesic module

This module contains the class, defining a general Geodesic:

class einsteinpy.geodesic.Geodesic(time_like, metric, coords, end_lambda, step_size=0.001, return_cartesian=True)[source]

Bases: object

Base Class for defining Geodesics

Parameters

  • time_like (bool) – Determines type of Geodesic True for Time-like geodesics False for Null-like geodesics

  • metric (*) – Metric, in which Geodesics are to be calculated

  • coords (*) – Coordinate system, in which Metric is to be represented

  • end_lambda (float) – Affine Parameter, Lambda, where iterations will stop Equivalent to Proper Time for Timelike Geodesics

  • step_size (float, optional) – Size of each geodesic integration step Defaults to 1e-3

  • return_cartesian (bool, optional) – Whether to return calculated values in Cartesian Coordinates Defaults to True

property state

Returns the Initial State Vector of the Geodesic

property trajectory

Returns the “Trajectory” of the Geodesic

calculate_trajectory(end_lambda=10.0, OdeMethodKwargs={'stepsize': 0.001}, return_cartesian=True)[source]

Calculate trajectory in spacetime, according to Geodesic Equations

Parameters

  • end_lambda (float, optional) – Affine Parameter, Lambda, where iterations will stop Equivalent to Proper Time for Timelike Geodesics Defaults to 10.0

  • OdeMethodKwargs (dict, optional) – Kwargs to be supplied to the ODESolver Dictionary with key ‘stepsize’ along with a float value is expected Defaults to {'stepsize': 1e-3}

  • return_cartesian (bool, optional) – Whether to return calculated values in Cartesian Coordinates Defaults to True

Returns

  • ~numpy.ndarray – N-element numpy array containing Lambda, where the geodesic equations were evaluated

  • ~numpy.ndarray – (n,8) shape numpy array containing [x0, x1, x2, x3, v0, v1, v2, v3] for each Lambda

calculate_trajectory_iterator(OdeMethodKwargs={'stepsize': 0.001}, return_cartesian=True)[source]

Calculate trajectory in manifold according to geodesic equation Yields an iterator

Parameters

  • OdeMethodKwargs (dict, optional) – Kwargs to be supplied to the ODESolver Dictionary with key ‘stepsize’ along with a float value is expected Defaults to {'stepsize': 1e-3}

  • return_cartesian (bool, optional) – Whether to return calculated values in Cartesian Coordinates Defaults to True

Yields

  • float – Affine Parameter, Lambda, where the geodesic equations were evaluated

  • ~numpy.ndarray – Numpy array containing [x0, x1, x2, x3, v0, v1, v2, v3] for each Lambda

class einsteinpy.geodesic.Timelike(metric, coords, end_lambda, step_size=0.001, return_cartesian=True)[source]

Bases: einsteinpy.geodesic.Geodesic

Class for defining Time-like Geodesics

Parameters

  • metric (*) – Metric, in which Geodesics are to be calculated

  • coords (*) – Coordinate system, in which Metric is to be represented

  • end_lambda (float) – Affine Parameter, Lambda, where iterations will stop Equivalent to Proper Time for Timelike Geodesics

  • step_size (float, optional) – Size of each geodesic integration step Defaults to 1e-3

  • return_cartesian (bool, optional) – Whether to return calculated values in Cartesian Coordinates Defaults to True