Equivalence of JT Gravity and Near-extremal Black Hole Dynamics in Higher Derivative Theory

Two derivative Jackiw Teitelboim gravity theory captures the near horizon dynamics of higher dimensional near extremal black holes, which is governed by a Schwarzian action at the boundary in the near horizon region. The partition function corresponding to this boundary action correctly gives the statistical entropy of the near extremal black hole. In this paper, we study the thermodynamics of spherically symmetric four dimensional near extremal black holes in presence of arbitrary perturbative four derivative corrections. We find that the near horizon dynamics is again captured by a JT like action with a particular namely square of Ricci scalar higher derivative modification. Effectively the theory is described by a boundary Schwarzian action which gets suitably modified due to the presence of the higher derivative interactions. Near extremal entropy, free energy also get corrected accordingly.