Particle Production and Krylov Complexity of Circular Strings Near Black Hole Horizons

TL;DR

This paper investigates particle production and Krylov complexity of circular strings near black hole horizons, revealing that complexity and operator growth exhibit universal scaling behaviors in the near-horizon regime.

Contribution

It introduces a detailed analysis of quantum fluctuations, particle production, and operator growth for strings near black holes, highlighting the emergence of thermalized complexity scaling.

Findings

Particle production is significant only in the radial sector near the horizon.

Krylov complexity scales nontrivially only in the near-horizon thermalized regime.

Operator growth rate depends linearly on the initial position of the probe string.

Abstract

For an infalling circular string, we study particle production, Krylov complexity, Lanczos coefficients, and operator growth induced by quantum fluctuations. Using canonical quantization in the squeezed state formalism, we show that significant particle production arises only in the radial sector as the string approaches the black hole horizon, while angular modes remain weakly excited. Exploiting the equivalence between particle number and Krylov complexity for two mode states, we find that nontrivial complexity scaling emerges only in the near-horizon, effectively thermalized regime, where the state approaches a thermofield double form. In this limit, the particle number exhibits a polynomial dependence on the initial position of the probe string. We further identify a linear dependence of the operator growth rate on the initial position of the probe string, suggesting a universal scaling behavior of operator growth and providing support for the complexity volume correspondence.