Trapping, chaos and averaging in bubbling AdS spaces

TL;DR

This paper investigates chaos and ensemble averaging in bubbling AdS spaces by analyzing null geodesics, confirming chaos indicators, and exploring how averaging influences geodesic behavior, revealing similarities to black hole trapping and thresholds where averaging breaks down.

Contribution

It provides a detailed analysis of chaos in LLM geometries, demonstrating how ensemble averaging affects geodesic dynamics and draws parallels to black hole physics.

Findings

Chaotic scattering behavior confirmed in LLM geometries

Averaging reduces chaos, resembling black hole trapping

Existence of a threshold timescale where averaging fails

Abstract

We discuss chaos and ensemble averaging in 1/2 BPS bubbling $AdS$ spaces of Lin, Lunin and Maldacena (LLM) by studying trapped and escaping null geodesics and estimating their decay rates. We find typical chaotic scattering behavior and confirm the Pesin relation between escape rates, Lyapunov exponents and Kolmogorov-Sinai entropy. On the other hand, for geodesics in coarse-grained (grayscale) LLM geometries (which exhibit a naked singularity) chaos is strongly suppressed, which is consistent with orbits and escape rates averaged over microscopic backgrounds. Also the singularities in these grayscale geometries produce an attractive potential and have some similarities to black hole throats trapping geodesics for a long time. Overall, averaging over the ensembles of LLM geometries brings us closer toward the typical behavior of geodesics in black hole backgrounds, but some important differences remain, in particular the existence of a threshold timescale when the averaging fails.