Timelike BKL singularities and chaos in AdS/CFT

TL;DR

This paper explores timelike BKL singularities in AdS/CFT, modeling their approach as a billiard problem, revealing chaotic behavior in 3+1 dimensions that may relate to chaotic RG flows in dual field theories.

Contribution

It extends BKL singularity analysis to timelike cases within AdS/CFT, demonstrating chaotic dynamics in 3+1 dimensions and proposing a connection to chaotic RG flows.

Findings

Chaotic behavior persists in 3+1 dimensions for pure gravity.

Chaotic behavior likely disappears in higher dimensions.

Potential interpretation of singularities as chaotic RG flows in AdS/CFT.

Abstract

We study the nature of a family of curvature singularities which are precisely the timelike cousins of the spacelike singularities studied by Belinski, Khalatnikov, and Lifshitz (BKL). We show that the approach to the singularity can be modeled by a billiard ball problem on hyperbolic space, just as in the case of BKL. For pure gravity, generic chaotic behavior is retained in (3+1) dimensions, and we provide evidence that it disappears in higher dimensions. We speculate that such singularities, if occurring in AdS/CFT and of the chaotic variety, may be interpreted as (transient) chaotic renormalization group flows which exhibit features reminiscent of chaotic duality cascades.