# Visualizing Frame Dragging in Kerr Spacetime¶

## Importing required modules¶

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```

```
import numpy as np
from einsteinpy.geodesic import Nulllike
from einsteinpy.plotting import StaticGeodesicPlotter
```

## Setting up the system¶

Initial position & momentum of the test partcle

Spin of the Kerr Black Hole

Other solver parameters

Note that, we are working in *M*-Units (\(G = c = M = 1\)). Also, setting momentum’s \(\phi\)-component to negative, implies an initial retrograde trajectory.

```
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```
position = [2.5, np.pi / 2, 0.]
momentum = [0., 0., -2.]
a = 0.99
steps = 7440 # As close as we can get before the integration becomes highly unstable
delta = 0.0005
omega = 0.01
suppress_warnings = True
```

Here, `omega`

, the coupling between the hamiltonian flows, needs to be decreased in order to decrease numerical errors and increase integration stability. Reference: https://arxiv.org/abs/2010.02237.

Also, `suppress_warnings`

has been set to `True`

, as the error would grow exponentially, very close to the black hole.

## Calculating the geodesic¶

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```

```
geod = Nulllike(
metric="Kerr",
metric_params=(a,),
position=position,
momentum=momentum,
steps=steps,
delta=delta,
return_cartesian=True,
omega=omega,
suppress_warnings=suppress_warnings
)
```

## Plotting the geodesic in 3D¶

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```

```
sgpl = StaticGeodesicPlotter(bh_colors=("red", "blue"))
sgpl.plot(geod, color="indigo", title="3D View", aspect="equal")
sgpl.show()
```

## Plotting the geodesic in 2D¶

```
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```

```
sgpl = StaticGeodesicPlotter(bh_colors=("red", "blue"))
sgpl.plot2D(geod, coordinates=(1, 2), figsize=(10, 10), color="indigo") # Plot X vs Y
sgpl.show()
```

As can be seen in the plot above, the photon’s trajectory is reversed, due to frame-dragging effects, so that, it moves in the direction of the black hole’s spin, before eventually falling into the black hole.

Also, the last few steps seem to have a larger `delta`

, but that is simply because of huge numerical errors, as the particle has crossed the Event Horizon.