Confluent conformal blocks and the Teukolsky master equation

Understand

Quasinormal modes of usual, four dimensional, Kerr black holes are described by certain solutions of a confluent Heun differential equation.

• In this work, we express these solutions in terms of the connection matrices for a Riemann-Hilbert problem, which was recently solved in terms of the Painlev\'e V transcendent.
• We use this formulation to generate the small-frequency expansion for the angular spheroidal harmonic eigenvalue, and derive conditions on the monodromy properties for the radial modes.
• Using exponentiation, we relate the accessory parameter to a semi-classical conformal description and discuss the properties of the operators involved.