Quantum corrections to the near-extremal thermodynamics of (warped) BTZ black holes

Abstract

We study one-loop effects in the near-extremal thermodynamics of BTZ and warped BTZ black holes, with particular emphasis on the fate of eigenmodes that become zero modes in the extremal throat. Our analysis is formulated in three-dimensional Topologically Massive Gravity, a higher derivative theory characterized by the presence of a gravitational Chern--Simons term, and it makes use of the Newman--Penrose formulation. For BTZ, we compare the near-horizon computation with the full-geometry eigenvalue problem and identify how the Schwarzian and rotational sectors are lifted at small temperature. We then extend the same strategy to warped BTZ. We find that rotational modes are essential for a consistent near-extremal treatment of both BTZ and warped BTZ black holes, and cannot be discarded without first specifying the boundary conditions.