In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a four-dimensional charged Einstein–Gauss–Bonnet black hole. The perturbation of a massless scalar field in the black hole’s background is adopted. The quasinormal modes are gotten by the 6th order WKB approximation approach and shadow radius, respectively. When the value of the Gauss–Bonnet coupling constant increase, the values of the real parts of the quasinormal modes increase and those of the imaginary parts decrease. The coincidence degrees of quasinormal modes derived by the two approaches increases with the increase of the values of the Gauss–Bonnet coupling constant and multipole number. It shows the correspondence between the shadow and test field in the four-dimensional Einstein–Gauss–Bonnet–Maxwell gravity. The radii of the photon sphere and shadow increase with the decrease of the Gauss–Bonnet coupling constant.

The chaos bound in the near-horizon regions has been studied through the expansions of the metric functions on the horizon. In this paper, we investigate the influence of the angular momentum of a charged particle on the chaos bound around a charged Einstein-Euler-Heisenberg AdS black hole. The equilibrium positions are gotten by fixing the charge mass ratio of the particle and changing its angular momentum, and they gradually move away from the event horizon with the increase of the angular momentum. The specific spatial regions where the bound is violated are found. For the fixed cosmological constant and the large value of the Euler Heisenberg parameter, a smaller value of the angular momentum causes the violation. Although the angular momentum's value is small, its corresponding spatial region is not small. The Lyapunov exponent is gotten by calculating the eigenvalue of the Jacobian matrix in the phase space.

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In this paper, we investigate the influence of the angular momentum of a charged particle around non-extremal and extremal Einstein-Maxwell-Dilaton-Axion black holes on the Lyapunov exponent. The angular momentum's ranges and spatial regions where the bound of the exponent is violated are found for certain values of the rotation parameter and dilatonic constant of the black holes. This violation always exists when the rotation parameter is large enough and the rotation directions of the particle is opposite to those of the black holes. The spatial regions outside the extermal black hole for the violation is relatively large. In the near-horizon regions of the extremal black holes, the violation depends on the rotation directions of the black holes and particle, and does not depend on the value of the angular momentum.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

In this paper, we investigate the influence of the angular momentum of a charged particle on the bound for the Lyapunov exponent of the chaos in non-extreme and extreme Einstein-Maxwell-Dilaton-Axion black holes. The derivation of the exponent is relied on the effective potential of the particle. We find that when the angular momentum takes the specific values, the bound is violated at the certain distances from the event horizons. This violation always exists when the rotation parameter of the black holes is large enough and the rotation direction of the particle is opposite to that of the black holes. In the near-horizon regions, the violation of the bound is dependent on the rotation directions of the extreme black hole and particle, and independent on the value of the angular momentum of the particle in the non-extreme black hole.