schwarzschild module¶

This module contains the basic class for calculating time-like geodesics in Schwarzschild Space-Time:

class einsteinpy.metric.schwarzschild.Schwarzschild(sph_coords, M, time)

Class for defining a Schwarzschild Geometry methods

classmethod from_coords(coords, M, q=None, Q=None, time=<Quantity 0. s>, a=<Quantity 0. m>)

Constructor

Parameters
• coords (CartesianDifferential) – Object having both initial positions and velocities of particle in Cartesian Coordinates

• M (Quantity) – Mass of the body

• time (Quantity) – Time of start, defaults to 0 seconds.

calculate_trajectory(start_lambda=0.0, end_lambda=10.0, stop_on_singularity=True, OdeMethodKwargs={'stepsize': 0.001}, return_cartesian=False)

Calculate trajectory in manifold according to geodesic equation

Parameters
• start_lambda (float) – Starting lambda(proper time), defaults to 0, (lambda ~= t)

• end_lamdba (float) – Lambda(proper time) where iteartions will stop, defaults to 100000

• stop_on_singularity (bool) – Whether to stop further computation on reaching singularity, defaults to True

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

• return_cartesian (bool) – True if coordinates and velocities are required in cartesian coordinates(SI units), defaults to False

Returns

• ~numpy.ndarray – N-element array containing proper time.

• ~numpy.ndarray – (n,8) shape array of [t, x1, x2, x3, velocity_of_time, v1, v2, v3] for each proper time(lambda).

calculate_trajectory_iterator(start_lambda=0.0, stop_on_singularity=True, OdeMethodKwargs={'stepsize': 0.001}, return_cartesian=False)

Calculate trajectory in manifold according to geodesic equation Yields an iterator

Parameters
• start_lambda (float) – Starting lambda, defaults to 0.0, (lambda ~= t)

• stop_on_singularity (bool) – Whether to stop further computation on reaching singularity, defaults to True

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

• return_cartesian (bool) – True if coordinates and velocities are required in cartesian coordinates(SI units), defaults to Falsed

Yields
• float – proper time

• ~numpy.ndarray – array of [t, x1, x2, x3, velocity_of_time, v1, v2, v3] for each proper time(lambda).