Equivalence of JT gravity and near-extremal black hole dynamics in higher derivative theory

Abstract

Abstract Two derivative Jackiw-Teitelboim (JT) 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 R2 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.