
I will argue that 2D Jackiw-Teitelboim (JT) gravity is a good approximation for some observables related to near extremal black holes in higher dimensions, beyond the semiclassical limit. In the first part of the talk I will apply this to the calculation of the density of states of charged black holes in 4D and give a resolution of the thermodynamic "mass gap" puzzle. In the second part, I will apply this to the calculation of the partition function and IR limit of boundary correlators of near extremal rotating BTZ in 3D. An independent boundary 2D CFT bootstrap argument shows that the emergence of a JT gravity sector is universal.