We investigate the frame dependence of the bound on the Lyapunov exponent for charged particles in the dilatonic Reissner-Nordström-anti–de Sitter (AdS) and Kerr-Sen-AdS black hole backgrounds, derived from the Einstein-Maxwell-dilaton theory and the low-energy effective action of heterotic string theory, respectively. A parallel analysis is performed across both the Einstein and string (Jordan) frames to examine the influence of the choice of frame on chaotic behavior. For massless particles, the Lyapunov exponent remains invariant under frame transformations, whereas for massive particles, it exhibits frame dependence owing to its coupling to the dilaton field. Our results demonstrate that the bound on chaos is not frame invariant and depends on the choice of frame. Depending on the various parameters, the bound can be satisfied in the Einstein frame and violated in the string frame, whereas the opposite situation may occur for different parameter values. Numerical computations corroborate the analytical findings and reveal the modifications in the chaotic behavior of string-inspired black holes induced by the dilaton field and the choice of frame.

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• Classical black holes
• Quantum aspects of black holes
• Quantum gravity