Analysis reveals how the Lyapunov exponent varies with black hole properties and particle characteristics, suggesting dynamic behaviors in extreme conditions.
We investigate the upper bound of the Lyapunov exponent for a charged particle in the Gibbons--Maeda--Garfinkle--Horowitz--Strominger (GMGHS)--AdS and Kerr--Sen--AdS black hole backgrounds, which originate from the low-energy effective actions of heterotic string theory and gauged supergravity. We analyze the Lyapunov exponent near the unstable orbit to examine possible violations of the bound. Our results indicate that the bound is sensitive to the signs and magnitudes of the charges, the angular momentum of the particle, the black hole spin, and the negative cosmological constant. The violations are pronounced in the extremal or near-extremal regime. Numerical analysis supports the analytical predictions and highlights the interplay between the string-inspired black hole and the charged particle.
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Lee et al. (2025) studied this question.
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