Visualizing Frame Dragging in Kerr Spacetime

Importing required modules

import astropy.units as u
import numpy as np
import matplotlib.pyplot as plt

from einsteinpy.coordinates import BoyerLindquistDifferential
from einsteinpy.geodesic import Timelike
from einsteinpy.metric import Kerr

Setting up metric and intial conditions

# Metric Parameters
M, a = 1.989e30 * u.kg, 0.3 * u.one

# Coordinate Object
bl = BoyerLindquistDifferential(
    t=0. * u.s,
    r=49.95e8 * u.m,
    theta=np.pi / 2 * u.rad,
    phi=np.pi * u.rad,
    v_r=0. * u.m / u.s,
    v_th=0. * u.rad / u.s,
    v_p=0. * u.rad / u.s
)

# Kerr Metric Object
mk = Kerr(coords=bl, M=M, a=a)

Calculating the geodesic

geod = Timelike(metric=mk, coords=bl, end_lambda=33932.90, step_size=1.2)

ans = geod.trajectory

x, y = ans[:,1], ans[:,2]

Plotting the geodesic

%matplotlib inline

fig = plt.figure(figsize=(12,10))
plt.scatter(x, y, s=0.2)
plt.scatter(0, 0)
plt.show()

As can be seen in the plot above, the test particle is dragged by the Kerr black hole.