Butterfly effect and $\textrm{T}\overline{\textrm{T}}$-deformation

TL;DR

This paper investigates shockwave geometries in holography with $ extrm{T}ar{ extrm{T}}$-deformed black holes, analyzing chaos indicators like OTOCs and butterfly velocities, and comparing different methods for consistency.

Contribution

It provides a detailed analysis of shockwave solutions in $ extrm{T}ar{ extrm{T}}$-deformed holographic models, exploring chaos bounds and their potential violations.

Findings

Potential violation of the Mezei-Stanford bound on butterfly velocity.

Consistency between shockwave, pole-skipping, and entanglement wedge methods.

Deformed geometries exhibit modified chaos characteristics.

Abstract

These notes present a comprehensive analysis of shockwave geometries in holographic settings, focusing on $\textrm{T}\overline{\textrm{T}}$-deformed BTZ black holes and their extensions. By constructing deformed metrics and employing Kruskal coordinates, we examine out-of-time-ordered correlators (OTOCs) as probes of quantum chaos. We also study localized shockwave solutions and analyze their backreaction, highlighting regimes in which the Mezei-Stanford bound on the butterfly velocity is potentially violated. The results obtained via shockwave methods are corroborated with recent developments in pole-skipping phenomena and the entanglement wedge approach, demonstrating consistency among distinct probes of chaos in holographic theories.