Microscopic entropy of regular BTZ black holes in 3d Lovelock gravity at all orders

Abstract

We give a microscopic derivation of the semi-classical entropy of the black holes of 3d Lovelock gravity with an infinite tower of regularized Lovelock corrections, which include the regular BTZ black holes found recently. Working in the mini-superspace formalism, we show that the reduced action and its boundary term can be obtained in closed form at all orders in terms of the generating function of the couplings. Assuming the ground state is described by the soliton obtained from the static black hole by a double Wick rotation, we compute the soliton mass and reproduce the semi-classical entropy from the Cardy formula without central charges for arbitrary couplings. We then extend the mini-superspace to stationary configurations, compute the mass and the angular momentum of the rotating black holes obtained by a boost, and verify the Cardy formula in the presence of rotation.