Abstract: In this talk I will consider a specific (near-)extremal limit of 4d Reissner–Nordström black holes (RNdS4), namely the Ultracold black hole. This regime is obtained when the cosmological horizon of de Sitter space and the black hole horizons merge together into the most constrained solution that a RNdS4 black hole can have.
After reviewing some essential features of this class of black holes, I will show how the Ultracold regime can be approached and highlight its classical properties.
I will then consider two possible avenues to study its quantum properties. One approach consists in dimensionally reducing the 4d theory to 2d, relating the resulting effective action to a known regime of Sine Dilaton gravity describing flat gravity in 2d. The latter is dual to DSSYK, an exactly solvable quantum model. A second approach consists in computing one-loop corrections to the 4d Euclidean gravitational path integral, a procedure which involves subtleties that I will take into account.