Universal Lyapunov bounds for rotating higher-dimensional black holes

Determine whether the dimension-dependent Lyapunov-exponent bounds derived for static, spherically symmetric higher-dimensional black holes extend to rotating higher-dimensional black holes, where null trapping is described by a photon region rather than a single photon sphere.

Background

The results in the paper rely on staticity and spherical symmetry, which reduce the relevant null-trapping structure to a single circular null orbit or photon sphere. Under these assumptions, the authors derive local and optical upper bounds on the orbit’s Lyapunov exponent.

For rotating higher-dimensional black holes, spherical symmetry is lost and null geodesics generally organize into a photon region. The authors therefore identify the extension of a universal instability bound to rotating geometries as a more difficult unresolved problem, requiring a framework that can handle the more complicated trapping structure.

References

Whether the same substitution disposes of the charged-particle violations above is an open question rather than a settled one, since no T_{\rm ind} has been constructed for those orbits.

— Classical and Quantum Chaos from Foundations to Holography  (2608.19131 - Shukla, 19 Aug 2026) in Section 6, subsection “Probe exponents and the chaos bound” (label sec:L6_bounds)

A more challenging extension concerns rotating higher-dimensional black holes. Once spherical symmetry is lost, null trapping is generally described by a photon region rather than a single photon sphere, making the construction of a universal instability bound considerably more involved. Investigating these extensions would help determine whether the bounds derived here reflect a more general property of black-hole spacetimes or are specific to the static, spherically symmetric setting considered in this work.

— Bounds on the Lyapunov Exponent of Circular Null Orbits in $n$-Dimensional Black-Hole Spacetimes  (2608.18436 - V. et al., 19 Aug 2026) in Summary and Discussion, final section