Chaos and fast scrambling delays of dyonic Kerr-Sen-AdS$_4$ black hole and its ultra-spinning version

TL;DR

This paper investigates the chaotic behavior and scrambling delays of dyonic Kerr-Sen-AdS4 black holes using holography, revealing bounds on Lyapunov exponents, effects of charges, and implications for fast scrambling in rotating black holes.

Contribution

It provides the first holographic analysis of chaos and scrambling delays in dyonic Kerr-Sen-AdS4 black holes, including ultra-spinning variants, with new bounds on Lyapunov exponents and charge-dependent delays.

Findings

Scrambling time scales logarithmically with entropy, supporting fast scrambling.

Lyapunov exponent bounded by a surface gravity-like quantity, approaching equality near extremality.

Electric and magnetic charges delay the scrambling process depending on shock wave charges.

Abstract

The scrambling time and its delay are calculated using holography in an asymptotically AdS black hole solution of the gauged Einstein-Maxwell-Dilaton-Axion (EMDA) theory, the dyonic Kerr-Sen-AdS$_4$ black hole, perturbed by rotating and charged shock waves along the equator. The leading term of the scrambling time for a black hole with large entropy is logarithmic in the entropy and hence supports the fast scrambling conjecture for this black hole solution, which implies that the system under consideration is chaotic. We also find that the instantaneous minimal Lyapunov index is bounded by $\kappa=2\pi T_H/(1-\mu\mathcal{L})$, which is analogous to the surface gravity but for the rotating shock waves, and becomes closer to equality for the near extremal black hole. For a small value of the AdS scale, we found that the Lyapunov exponent can exceed the bound for a large value of $\mathcal{L}$. Due to the presence of the electric and magnetic charge of the shock waves, we also show that the scrambling process of this holographic system is delayed by a time scale that depends on the charges of the shock waves. The calculations also hold for the ultra-spinning version of this black hole. The result of this paper generalizes the holographic calculations of chaotic systems which are described by an EMDA theory in the bulk.