Physicist Janna Levin last year published a paper where she offers a way to understand what happens to objects trapped in the intense gravitational field around rotating black holes. As this chart shows, there are many paths to the singularity.
Levin, who has also written a beautiful, fascinating book about physics called How the Universe Got Its Spots, gives a technical explanation of her periodic table of black hole orbits:
Understanding the dynamics around rotating black holes is imperative to the success of the future gravitational wave observatories. Although integrable in principle, test particle orbits in the Kerr spacetime can also be elaborate, and while they have been studied extensively, classifying their general properties has been a challenge. This is the first in a series of papers that adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We define a taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strong-field regime. Instead, eccentric orbits trace out precessions of multi-leaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some point in the strong-field regime past which zoom-whirl behavior becomes unavoidable. Finally, we sketch the potential application of the taxonomy to problems of astrophysical interest, in particular its utility for computationally intensive gravitational wave calculations.
Kerr black holes are black holes that rotate, and that affects the gravity waves they generate. I love these charts of the many possible ways that objects might approach, orbit, and eventually get swallowed by a black hole. If you want to delve into the math Levin used to create these images, check out the whole paper. It's free online.
"A Periodic Table for Black Hole Orbits" via arXiv