Near extremal Black Holes, extended hydrodynamics and quantum gravitational effects

by Elias Kiritsis

Tuesday 14 Apr 2026, 14:00 → 16:00 Europe/Rome

Charged asymptotically AdS black holes are known to be dual to strongly coupled QFTs at finite density. In the near-extremal limit, where temperature is much smaller that the charge density , they are known to develop an IR scaling symmetry encoded in the near horizon AdS2 geometry.

It has also been argued that the low energy dynamics associated with such black holes, which is hydrodynamics, is valid at much higher energies and momenta than what is conventionally assumed. We show concrete evidence of this by comparing exact charge and energy correlators to various improved hydrodynamic approximations that resum the effect of non-trivial AdS2 poles 

When the transverse space to the AdS2 geometry has finite volume, there is a non-zero energy scale Egap, scaling as 1/charge for large charge, below which quantum-gravitational corrections due to the fluctuations of the nearly-gapless Schwarzian modes become important. Such corrections to the retarded Green's function are calculated at different relative values of  the frequency , T, and Egap. The frequency ->  0 limit is used to define the shear viscosity eta. As the temperature is lowered below the charge density, quantum corrections are found to increase the value of eta with respect to its famous semiclassical   result  and  the shear viscosity diverges as 1/sqrt{T} at T << Egap. The quantum result for the ratio eta/s, where s is the entropy density, dips below the semiclassical limit of 1/4 pi when Egap<< T << mu, then turns back to increase towards lower temperatures, and finally diverges at temperatures much below Egap.

Comments on the similarity of near-extremal black holes and glasses as well as their effect on the Aretakis instability will be advanced.