Python Packages to Calculate orbits in Schwarzschild Metric

[Arman777]

I am looking for a Python Code/Package to calculate the orbits of the time-like and null-like particles in Schwarzschild metric (in spherical coordinates)

Does anyone know such package ?

Note: I am mostly looking for packages to calculate the RIGHT side of the given images (i.e the orbits in $(r, \phi)$ plane.

Note 2: If you guys want to share not python but something else that's also okay.

 

[pbuk]

Let me google that for you

 

[Arman777]

I did that but did not finding useful. there's Einsteinpy but it does in terms of momentum and initial position instead of energy. I am not sure what values should I put to produce those graphs.

import numpy as np

from einsteinpy.geodesic import Timelike
from einsteinpy.plotting.geodesic import GeodesicPlotter

position = [40., np.pi / 2, 0.]
momentum = [0., 0., 3.83405]
a = 0.
steps = 5500
delta = 1.

geod = Timelike(
    metric="Schwarzschild",
    metric_params=(a,),
    position=position,
    momentum=momentum,
    steps=steps,
    delta=delta,
    return_cartesian=True
)

gpl = GeodesicPlotter()
gpl.plot2D(geod, coordinates=(1, 2)) # Plot X & Y
gpl.show()

https://docs.einsteinpy.org/en/stable/examples/Visualizing Precession in Schwarzschild Spacetime.html

This produces something like the 2nd image. But how about 1,3 and 4 ?

 

[Ibix]

Is my code (for Kerr spacetime, but just set $a=0$) more like what you want? I think I set it up so you can initialise it in various ways.

 

[Arman777]

Is my code (for Kerr spacetime, but just set $a=0$) more like what you want? I think I set it up so you can initialise it in various ways.

Well if you think that it can produce the images shown above for a given metric then yes. I can use it

 

[Ibix]

Well I don't think you can get the effective potential out of it, but you should be able to get the orbits.

 

[Arman777]

Well I don't think you can get the effective potential out of it, but you should be able to get the orbits.

Thats also good. So what should I type to produce those images ? I mean how can I run the code ?