Spherical photon orbits around Kerr (what I did this week)

Did you know that light can orbit a black hole?

These orbits are unstable: give your photon a tiny push in or out and it will either plunge into the horizon or shoot out to infinity. It's like trying to balance a pencil on its tip: you have to perfectly tune these orbits.

But still! Light can orbit a black hole. Ever wondered what these trajectories look like?

I spent a bit of time this past week making a simulator for spherical photon trajectories around rotating black holes (this is part of the reason why I'm behind on my posts here; sorry!). Now you can easily see all these trajectories in your browser, just by dragging around the slider controls.

Besides being unstable, these orbits generally fill the whole (truncated) sphere of allowed locations. That's because generically, the frequencies of azimuthal motion and longitudinal motion are incommensurate. But, rationals are dense in the reals, so there are actually resonant orbits all over parameter space. This means the orbits recur. They can be really pretty! Here's a picture of one of the 4:3 resonances:

Studying the frequency ratios and locations of resonances is also really cool. Those are encoded in this colorful contour plot. To understand what this plot means, I recommend that you head there now to play with the simulation, and read a lot more about the physics!