Exact solution of Kerr black hole perturbations via and instanton counting: Greybody factor, quasinormal modes, and Love numbers
Giulio Bonelli (International School of Advanced Studies (SISSA) via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste Institute for Geometry and Physics, IGAP, via Beirut 2, 34136 Trieste, Italy); Cristoforo Iossa (International School of Advanced Studies (SISSA) via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste Institute for Geometry and Physics, IGAP, via Beirut 2, 34136 Trieste, Italy); Daniel Panea Lichtig (International School of Advanced Studies (SISSA) via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste Institute for Geometry and Physics, IGAP, via Beirut 2, 34136 Trieste, Italy); Alessandro Tanzini (International School of Advanced Studies (SISSA) via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste Institute for Geometry and Physics, IGAP, via Beirut 2, 34136 Trieste, Italy)
We give explicit expressions for the finite frequency greybody factor, quasinormal modes, and Love numbers of Kerr black holes by computing the exact connection coefficients of the radial and angular parts of the Teukolsky equation. This is obtained by solving the connection problem of the confluent Heun equation in terms of the explicit expression of irregular Virasoro conformal blocks as sums over partitions via the Alday, Gaiotto, and Tachikawa correspondence. In the relevant approximation limits our results are in agreement with existing literature. The method we use can be extended to solve the linearized Einstein equation in other interesting gravitational backgrounds.