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

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