Jackiw-Teitelboim gravity and near-extremal BTZ thermodynamics

We study the near horizon 2D gravity theory which captures the near extremal thermodynamics of Banados-Teitelboim-Zanelli (BTZ) with excess mass δM and excess angular momentum δJ=LδM over extremality. We find that the Jackiw-Teitelboim theory is able to capture such departures from extremality with an additional parameter L relating it to the near extremal BTZ configuration. We are able to show this by obtaining new simultaneous near horizon near extremal limits of the BTZ geometry parametrized by L. The resulting Jackiw-Teitelboim theory captures the near extremal thermodynamics of such BTZ geometries provided we identify the temperature TH⁽²⁾ of the AdS₂ geometry in the Jackiw-Teitelboim theory to be TH⁽²⁾=TH/(1-μL), where TH is the BTZ temperature and μ its chemical potential with μL<1.