I want to find a quantum field theory whose low-energy limit describes a Kerr black hole.
Maldacena duality suggests that I should look for a (2+1)-dimensional strongly-interacting quantum field theory with many degrees of freedom. Kitaev's coherent-scrambling conjecture further suggests that I require the field theory's out-of-time-ordered 4-point functions to decay exponentially with exponent 2pi T, with the temperature T determined by eigenstate thermalization.
But before getting to quantum field theory, I had to engage the (3+1)-dimensional classical geometry. So far, I have successfully calculated the backreaction from a massless particle on the horizon of a rotating (3+1)-dimensional black hole (Kerr-Newman and Kerr-AdS)-this is the rotating generalization of the Dray-'t Hooft gravitational shockwave.
Despite the Dray-'t Hooft result being decades old, I think that its physical significance remains unclear. I would like to revisit this with a more robust formalism for nonequilibrium field theory: The Feynman-Vernon-Schwinger-Keldysh path integral. I plan to apply it to perturbation theory around the Kerr and Kerr-AdS spacetimes and see whether I can improve on standard treatments of Hawking radiation.