Visualizing frame dragging in Kerr space-time

Importing required modules

from astropy import units as u
import numpy as np
from einsteinpy.metric import Kerr

Defining position/velocity of test particle

• Initial velocity is kept 0

M = 1.989e30 * u.kg
pos_vec = [50e5 * u.km, np.pi / 2 * u.rad, np.pi * u.rad]
vel_vec = [0 * u.km / u.s, 0 * u.rad / u.s, 0 * u.rad / u.s]

end_lambda = ((1 * u.year).to(u.s)).value / 930
# Choosing stepsize for ODE solver to be 0.02 minutes
stepsize = ((0.02 * u.min).to(u.s)).value

starting_time = 0 * u.s
a = 0.3
obj = Kerr.from_BL(pos_vec, vel_vec, starting_time, M, a)
ans = obj.calculate_trajectory(
    end_lambda=end_lambda, OdeMethodKwargs={"stepsize": stepsize}, return_cartesian=True
)
x, y = ans[1][:,1], ans[1][:,2]

Plotting the trajectory

%matplotlib inline

import matplotlib.pyplot as plt
plt.scatter(x,y, s=0.2)
plt.scatter(0,0, c='black')
plt.show()

It can be seen that as the particle approaches the massive body, it acquires axial velocity due to spin and frame-dragging effect of the body.