I have a long-term interest in exploring how classical (i.e., non-quantum) relativistic strings interact with black holes. With Heling Deng, Andrei Gruzinov, Alex Vilenkin, and Hengrui Xing, I have studied the dynamics of a string loop captured by a Kerr black hole.
Spinning black holes as cosmic string factories
In this first paper (which grew out of Hengrui Xing's undergraduate project, but went well beyond its original scope), we created an analytical formalism for the evolution of the captured loop. We made extensive use of the results obtained by Valeri Frolov and his collaborators for asymptotically straight strings interacting with Kerr black holes. It allowed us to infer many things: the growth of loops by superradiance, their shrinking by horizon friction, and their ultimate fate. This paper had some very fun mathematical physics. The loop can be represented by a closed "auxiliary" curve in 3-D space which evolves secularly. The evolution of the auxiliary curve has direct connections to the work of mathematicians like Richard Hamilton, and its geometrical "events", like self-intersections, have direct physical significance. I am ridiculously proud of this paper, but it has a major caveat: it neglected the depletion of the loops through string reconnections and ejections of daughter loops. This is still an open problem.
Simulating cosmic string loop captured by a rotating black hole
In the second paper, Heling Deng, with considerable technical advice from Andrei Gruzinov, managed to perform a direct numerical simulation of the loop motion in Kerr spacetime (Alex and I contributed through discussions and cheerleading). Very importantly, he confirmed that the formalism developed in the previous paper was accurate in its supposed domain of validity, and gave qualitatively reasonable results even in cases where it was not expected to be accurate. I feel like the two papers together form a good foundation for further exploration of this topic.
Cosmic Strings and Primordial black holes
Alex, Andrei and I also wrote a paper on the cosmological scenario where primordial black holes get incorporated into the string network. One interesting aspect of this scenario is the production of oscillating objects consisting of several black holes connected and held together by strings.