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

Abstract: We investigate the frame dependence of the Lyapunov exponent bound for charged particles in dilatonic Reissner-Nordstr\"om-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.