Lyapunov bounds in Einstein-Gauss-Bonnet and Lovelock gravity

Establish whether a dimension-dependent upper bound on the Lyapunov exponent of circular null orbits can be derived in Einstein-Gauss-Bonnet and more general Lovelock theories, whose modified field equations alter the relations among matter variables, metric functions, and the photon-sphere characteristic function.

Background

The paper derives a dimension-dependent upper bound on the Lyapunov exponent of unstable circular null geodesics for static, spherically symmetric, asymptotically flat black holes in n-dimensional Einstein gravity. The derivation depends on the Einstein field equations and the tangential null energy condition, which together control the derivative of the photon-sphere characteristic function.

The authors identify Einstein-Gauss-Bonnet and Lovelock theories as natural higher-dimensional extensions. Although photon-sphere-radius bounds have been studied in these theories, the paper leaves unresolved whether analogous Lyapunov-exponent bounds can be obtained after accounting for the modified gravitational field equations.

References

An important direction is to extend the analysis beyond Einstein gravity. Einstein-Gauss-Bonnet and, more generally, Lovelock theories are particularly relevant in higher dimensions. The modified field equations change the relation between the matter variables, the metric functions, and the photon-sphere characteristic function. Although bounds on the photon-sphere radius have already been studied in these theories, it remains to be seen whether a corresponding dimension-dependent bound on the Lyapunov exponent can be established.

— 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