Physical constraints on the MSS chaos-bound in black hole spacetimes

TL;DR

The paper develops a self-consistent framework to assess the MSS chaos bound for test particles in black hole spacetimes by fixing the angular momentum strictly from the underlying geometry. Using the Jacobi method and an effective-potential approach, it shows that apparent chaos-bound violations in the charged Kiselev spacetime disappear when L0 is determined from r0, clarifying the role of orbital parameters. Extending the analysis to AdS black holes in quadratic f(R) gravity reveals genuine violations at large charge-to-mass ratios caused by curvature corrections, not orbital choices, illustrating that the MSS bound is not universally preserved in curvature-extended theories. Overall, the work provides a systematic way to distinguish apparent from physical chaos and highlights how holography, causality, and higher-curvature terms influence chaos diagnostics in gravitational systems.

Abstract

Chaotic motion near black holes has recently been examined through the lens of the Maldacena-Shenker-Stanford (MSS) chaos-bound, but reported violations remain contradictory. A major source of this ambiguity lies in the common practice of treating the angular momentum of test particles as a freely adjustable parameter, rather than a quantity fixed by the circular-orbit conditions. In this work, we develop a fully constrained framework in which the angular momentum of particles is determined exactly from the underlying geometry and is used consistently in both the orbital and Lyapunov analyses. For the charged Kiselev black hole, previously reported chaos-bound violations disappear under a consistent treatment of angular momentum, indicating that these effects are apparent rather than physical. This inference is reinforced by the exact agreement between our results and the standard circular-orbit condition obtained from the effective-potential approach. By extending the analysis to geometries containing higher-order curvature terms, we find genuine chaos-bound violations at large charge-to-mass ratios, originating from curvature corrections rather than orbital parameters. This framework, therefore, provides a systematic means of distinguishing apparent from physical chaos-bound violations in Einstein gravity and its extensions.

Figures (1)

• Figure 1: Apparent violations of the chaos-bound for fixed parameters $m = 2$, $q = 15$, and $Q = 1.95$. Here, we present different curves corresponding to different values of the normalization constant $\alpha$, such as for $\alpha=0.02$ (solid black curve), $\alpha=0.06$ (dotted blue curve), and $\alpha=0.096$ (dashed red curve). Unrealistically high angular momentum leads to orbits very close to the horizon, causing apparent violations. However, these apparent violations disappear when the angular momentum is determined self-consistently from the circular orbit condition as given in Table \ref{['tab:tjac']}.