2026/07/23 by Xiang Li, Haiming Yuan, Xian-Hui Ge
#hep-th #gr-qc
We develop a systematic analytic method for studying high-order pole-skipping in near-extremal holographic black holes. In the near-extremal regime, approaching the limit T→0, the near-horizon geometry develops an approximately AdS2 × ℝd-1 structure; we show that the mode index q labeling pole-skipping points is identified with the IR conformal dimension ΔIR = q in the emergent AdS2/CFT1 correspondence, providing a concrete physical interpretation of the subleading pole-skipping tower. The method reorganizes the near-horizon Frobenius expansion according to powers of temperature. This reveals a temperature-graded hierarchical structure that reduces the n-th-order pole-skipping condition to a factorized algebraic equation:each pole-skipping momentum depends only on the mode index q, not on the order n. This n-independence produces a high degeneracy as T→ 0, where pole-skipping momenta at all orders collapse onto a discrete set of values determined by near-horizon geometry and the scalar field mass; these values can be expressed in terms of thermodynamic quantities such as entropy density and specific heat. In the limit n ≫ 1 (with nT remaining small), the leading pole-skipping momenta grow asymptotically as kn,n ∝ n. We compute leading temperature corrections and verify our predictions through numerical analysis of the Dyonic Gubser--Rocha model. The results confirm that high-order pole-skipping at low temperature is governed by near-horizon physics. This provides analytic access to pole-skipping points well beyond those accessible by standard determinant methods and clarifies the structure of holographic Green's functions in the low-temperature regime.