In this talk, I will show how one can study gravitational perturbations from the near-horizon region of extremal and near-extremal rotating black holes in a general higher-derivative extension of Einstein gravity. I will explain how the near-horizon Teukolsky equation is modified via a correction to the angular separation constant. The near-horizon region also provides constraints on the form of the full modified Teukolsky radial equation, which serve as a stepping stone towards the study of quasinormal modes of near-extremal black holes. In the second part of the talk, I will present a new family of EFT, motivated by preserving two fundamental properties of GR: gravitational waves are non-birefringent, and black hole quasinormal modes are isospectral. This leads to a novel class of EFT extensions, which remarkably, coincides with predictions from string theory and implies a previously unknown feature of string theory effective actions.

Significant progress has been made regarding the microstate counting of extremal AdS black holes in the context of AdS/CFT, where the Cardy-like limit on the field side theory has often been used. I will discuss the implications of this limit on the gravity side and how it translates to a parameter space limit on the black hole solution. This limit, referred to as the gravitational Cardy limit, is applied to the Bardeen Horowitz near-horizon geometry to reproduce the Bekenstein-Hawking entropy via the Kerr/CFT correspondence, yielding a third approach to the computation of the entropy. Relaxing the gravitational Cardy limit, the computation can be further extended to near-extremality, where the heat capacity is found. For each case, extremal and near-extremal, the entropy from these different approaches match, providing a unique and universal expression for the entropy. https://zoom.us/j/98264204601?pwd=Z0xYdG1vVlEwU1M1bDhVcXQvWURPQT09