Applied SUSY QFT & BHPT: one loop corrections to near extremal (dS-)Kerr thermodynamics

The study of Black-Hole perturbation theory [BHPT] is a classical problem in General Relativity and crucial to study gravitational waves. As the high order of symmetry of the BH gravitational field implies separation of variables, BHPT reduces to the study of 2nd order linear ordinary differential equations (ODE).

These ODEs have particular rational potentials and are solved exactly by classical Virasoro conformal blocks. The latter have an explicit expression because of AGT duality (BPS sector in susy gauge theory ≡CFT2) and the classical limit of crossing relations generate the explicit solution of the connection problem of the ODE. Applying the solution back to BHPT one gets a powerful computational technique.

Quantitative and qualitative (exact) results in BHPT have been obtained so far, such as grey-body factors, Love numbers, quasi-normal modes, BH scattering amplitudes, effective actions in BH backgrounds. In particular, combining with a generalisation of the Gelfand-Yaglom formula for singular potentials one gets an exact expression for the one loop (dS-)Kerr effective action. The latter is shown to undergo a precise scaling with the temperature and proves a conjecture made by means of qualitative arguments on one-loop corrections to the entropy.