JT gravity and near-extremal thermodynamics for Kerr black holes in AdS4,5 for rotating perturbations

A bstract We study the near horizon 2d gravity theory which captures extremal thermodynamics of Kerr black holes where a linear combination excess angular momentum δJ and mass δM is held fixed. These correspond to processes both momenta are perturbed leaving them extremal. For AdS 4 we hold $$ \delta J-\mathcal{L}\delta M=0 δJ − L δM = 0 while for Myers-Perry(MP) type hole in 5 {J}_{\varphi 1,2}-{\mathcal{L}}_{\varphi 1,2}\delta δ J φ 1 , 2 . show that horizon, Jackiw-Teitelboim able capture higher dimensional at small temperatures T H this by generalizing limits found literature parameters \mathcal{L} {\mathcal{L}}_{\varphi 1,2} two geometries. The resulting JT such geometries provided identify temperature {T}_H^{(2)} T H 2 geometry be {T}_H^{(2)}={T}_H/\left(1-\mu \mathcal{L}\right) / μ 4d {T}_h^2={T}_H/\left(-\mu \left({\mathcal{L}}_{\varphi 1}+{\mathcal{L}}_{\varphi 2}\right)\right) h + 5d μ their chemical potential, with \mu \mathcal{L}<1 < 2}\right)<1 respectively. also argue embeds itself non-trivially dual