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Frame Dependence of Bound on Lyapunov Exponent in Dilatonic Reissner-Nordström-AdS and Kerr-Sen-AdS Black Holes

Hocheol Lee, Bogeun Gwak

TL;DR

The paper addresses whether the chaos bound for Lyapunov exponents is frame-invariant in string-inspired black holes by comparing Einstein and string frames in dilatonic RN--AdS and Kerr--Sen--AdS spacetimes. It derives and contrasts the effective Lagrangians in the two frames, showing massless particles yield identical Lyapunov exponents while massive particles generally do not due to dilaton couplings, and defining the bound via $\Delta^2 = \kappa^2 - \lambda^2$. Across extremal/non-extremal and asymptotically flat/AdS cases, the authors map regions where the bound is satisfied or violated, with large angular momentum often yielding frame-independent results. Numerical results corroborate the analytic expressions and reveal parameter regimes where frame-dependence is pronounced, offering insights into holographic chaos, conformal-frame choices, and string-dilaton effects on chaotic dynamics.

Abstract

We investigate the frame dependence of the Lyapunov exponent bound for charged particles in dilatonic Reissner-Nordström-AdS and Kerr-Sen-AdS black hole backgrounds, derived from Einstein-Maxwell-dilaton theory and the low-energy effective action of heterotic string theory, respectively. The analysis is performed in both the Einstein and string (Jordan) frames to examine the influence of conformal transformations on chaotic behavior. For massless particles, the Lyapunov exponent remains invariant under frame transformations, whereas for massive particles, it exhibits frame dependence owing to coupling to the dilaton field. Our results indicate sensitivity of the bound on chaos to the choice of frame. Depending on various parameters, the bound can be satisfied in the Einstein frame and violated in the string frame, while the opposite situation may occur for different parameter values. Numerical computations corroborate the findings of our analysis and demonstrate modifications in the chaotic behavior of string-inspired black holes induced by the dilaton field and the choice of frame.

Frame Dependence of Bound on Lyapunov Exponent in Dilatonic Reissner-Nordström-AdS and Kerr-Sen-AdS Black Holes

TL;DR

The paper addresses whether the chaos bound for Lyapunov exponents is frame-invariant in string-inspired black holes by comparing Einstein and string frames in dilatonic RN--AdS and Kerr--Sen--AdS spacetimes. It derives and contrasts the effective Lagrangians in the two frames, showing massless particles yield identical Lyapunov exponents while massive particles generally do not due to dilaton couplings, and defining the bound via . Across extremal/non-extremal and asymptotically flat/AdS cases, the authors map regions where the bound is satisfied or violated, with large angular momentum often yielding frame-independent results. Numerical results corroborate the analytic expressions and reveal parameter regimes where frame-dependence is pronounced, offering insights into holographic chaos, conformal-frame choices, and string-dilaton effects on chaotic dynamics.

Abstract

We investigate the frame dependence of the Lyapunov exponent bound for charged particles in dilatonic Reissner-Nordström-AdS and Kerr-Sen-AdS black hole backgrounds, derived from Einstein-Maxwell-dilaton theory and the low-energy effective action of heterotic string theory, respectively. The analysis is performed in both the Einstein and string (Jordan) frames to examine the influence of conformal transformations on chaotic behavior. For massless particles, the Lyapunov exponent remains invariant under frame transformations, whereas for massive particles, it exhibits frame dependence owing to coupling to the dilaton field. Our results indicate sensitivity of the bound on chaos to the choice of frame. Depending on various parameters, the bound can be satisfied in the Einstein frame and violated in the string frame, while the opposite situation may occur for different parameter values. Numerical computations corroborate the findings of our analysis and demonstrate modifications in the chaotic behavior of string-inspired black holes induced by the dilaton field and the choice of frame.
Paper Structure (18 sections, 113 equations, 6 figures, 2 tables)

This paper contains 18 sections, 113 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Review of Lyapunov Exponent
  3. Frame Dependence of Lyapunov Exponent
  4. Dilatonic Reissner--Nordström--AdS Black Hole
  5. Asymptotically Flat Spacetime
  6. Extremal Case
  7. Non-Extremal Case
  8. Asymptotically AdS Spacetime
  9. Extremal Case
  10. Non-Extremal Case
  11. Kerr--Sen--Ads Black Hole
  12. Asymptotically Flat Spacetime
  13. Extremal Case
  14. Non-Extremal Case
  15. Asymptotically AdS Spacetime
  16. ...and 3 more sections

Figures (6)

  • Figure 1: Bound on chaos in the near-horizon limit with vanishing angular momentum of extremal dilatonic Reissner--Nordström--AdS black hole backgrounds.
  • Figure 2: Bound on chaos in the large angular momentum limit of extremal dilatonic Reissner--Nordström--AdS black hole backgrounds.
  • Figure 3: Bound on chaos in the large angular momentum limit of non-extremal Kerr--Sen black hole backgrounds.
  • Figure 4: Bound on chaos in the near-horizon limit with vanishing angular momentum for extremal Kerr--Sen--AdS black hole backgrounds.
  • Figure 5: Bound on chaos in the extremal Kerr--Sen--AdS black hole background.
  • ...and 1 more figures