# CMT for extremal BH An extremal black hole in AdS corresponds to the zero-temperature limit of a boundary field theory via [[0001 AdS-CFT|holography]]. There is a subtlety in understanding [[0429 Hydrodynamics|hydrodynamics]] at zero temperature: $\omega\to0$ and $T\to0$ does not commute, so cannot just take a naive limit of finite-temperature results. ## Refs - parent page: [[0432 AdS-CMT]] - [[0340 Aretakis instability]] - Kerr - [[2017#Gralla, Zimmerman]] - [[2018#Casals, Zimmerman]] - planar - [[2018#Gralla, Ravishankar, Zimmerman]] - BTZ - [[2019#Gralla, Ravishankar, Zimmerman]] - [[0325 Quasi-normal modes|QNM]] - [[1998#Freedman, Mathur, Matusis, Rastelli]] - [[ChalmersNastaseSchalmSiebelink1998]]: hep-th/9805105 - [[0473 Retarded Green's function]] - scalar and fermionic operators: [[2009#Faulkner, Liu, McGreevy, Vegh]] - vector (charge current) and tensor (energy-momentum) operators: [[2009#Edalati, Jottar, Leigh]] - [[0179 Pole skipping|pole skipping]] - [[2020#Natsuume, Okamura]] - extremal non-relativistic backgrounds - [[ImeroniSinha2009]][](http://arxiv.org/abs/0907.1892) - [[AdamsBrownDeWolfeRosen2009]][](http://arxiv.org/abs/0907.1920) - zero-temperature [[0431 Holographic superconductor|holographic superconductor]] - [[2009#Horowitz, Roberts]]