Construction of bulk solutions for towers of pole-skipping points

Abstract

The pole-skipping phenomenon has been proposed as a connection between chaotic properties of black hole geometries and special points where regular solutions of linearized Einstein equations at horizons have extra free parameters. In this work, we pursue the special points in the near-horizon analysis of integer spin-$\ell$ fields on the Rindler-AdS black hole. We construct linear combinations of field components to simplify coupled equations of massive fields and investigate towers of the special points along with imaginary Matsubara frequencies $i\omega =2\pi (n+1-\ell )T$ with a non-negative integer $n$ and the Hawking temperature $T$. We also propose that integrals of spin-$\ell$ bulk propagators over horizons of static black holes capture behaviors at the special points, which are generalizations of integrals of graviton propagators for shock wave geometries. Their interpretation is provided in terms of four-point amplitudes with the spin-$\ell$ exchange.

27 pages, 3 figures. v2: introduction improved

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• Pole-Skipping in Rotating BTZ Black Holes
• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Pole-skipping of Holographic Correlators: Aspects of Gauge Symmetry and Generalizations
• Pole-skipping and chaos in D3-D7 brane systems
• Pole-skipping for massive fields and the Stueckelberg formalism
• Effect of scalar condensation on fermionic pole-skipping