Crossover from Schwarzian dynamics to rotational soft modes in near-extremal Lovelock black holes

Abstract

Near-extremal black holes are controlled by a small set of soft modes, and counting these modes fixes the coefficient of $\log T$ in the entropy. We ask whether genuine six-derivative interactions change that count, working in seven-dimensional third-order Lovelock gravity, the simplest setting where the cubic Lovelock term is dynamical. The multiplicities stay the same, but the naive count fails. At fixed charge the Maxwell mode is frozen out, and the fifteen rotational modes of the $S^5$ act as a quantum rotor that only switches on above the scale $K_J^{-1}$. As a result, the coefficient of $\log T$ runs from $3/2$ at the lowest temperatures to $9$ above that scale, and never reaches the naive Gaussian value $19/2$. We compute the moment of inertia $K_J$ from the charged slow-rotation solution and find that the Lovelock couplings move the crossover without changing the multiplicities. Only large AdS black holes have a wide window in which the full rotational contribution competes with the classical entropy. Adding a probe charged scalar, we derive an analytic near-horizon Schwinger threshold in the cubic coupling. Its large-AdS limit tells us when the broad rotational crossover window can coexist with the absence of a charged-scalar Breitenlohner--Freedman (BF) bound violation.