AI 中文总结
该研究将四维黑洞圆形零轨道李雅普诺夫指数的模型无关上界分析，扩展到任意维静态球对称渐近平坦黑洞，推导了依赖时空维度的上界，相关界在n=4时退化为已知结果，且部分界在Schwarzschild-Tangherlini真空解中饱和，为时空维度与光子捕获不稳定性提供了一致性条件。
AI 中文摘要
不稳定圆形零轨道为黑洞光学、光子环、强引力透镜与准正则振铃的 eikonal 扇区提供了几何桥梁。在四维爱因斯坦引力中，当物质 sector 满足标准能量条件时，此类轨道的不稳定性率（以李雅普诺夫指数λ衡量）服从与模型无关的上界。我们将此分析扩展到任意维爱因斯坦引力中的静态、球对称、渐近平坦黑洞，允许各向异性物质分布。我们证明，在切向零能量条件下，李雅普诺夫指数可得到一个依赖于维度的上界，该上界由光子球 r=r_γ 处的广义表面引力κ(r)和度规函数μ(r)给出。对于n维黑洞时空，该界为λ≤√(n-3) κ_γ/√μ_γ。我们还基于临界碰撞参数（阴影半径）、轨道频率、局部加速度尺度及 eikonal 准正则模阻尼推导了相关界。所有主不等式在n=4时均退化为已知的四维结果。此外，包含临界碰撞参数和轨道频率的界在Schwarzschild-Tangherlini真空解中达到饱和。这些结果提供了一组紧凑的一致性条件，将时空维度与爱因斯坦引力中光子捕获的不稳定性联系起来。
英文摘要
Unstable circular null orbits provide a geometric bridge between black-hole optics, photon rings, strong gravitational lensing, and the eikonal sector of quasinormal ringing. In four-dimensional Einstein gravity, the instability rate of such orbits, measured by the Lyapunov exponent $λ$, obeys model-independent upper bounds when the matter sector satisfies standard energy conditions. We extend this analysis to static, spherically symmetric, asymptotically flat black holes in arbitrary dimensional Einstein gravity, allowing for an anisotropic matter distribution. We show that, under the tangential null energy condition, the Lyapunov exponent admits a dimension-dependent upper bound in terms of the generalized surface gravity $κ(r)$ and the metric function $μ(r)$, both evaluated at the photon sphere $r =r_γ$. For $n$- dimensional black hole spacetime, the bound is $λ\leq\sqrt{n-3}\, {κ_γ}/{\sqrt{μ_γ}}$. Related bounds are derived in terms of the critical impact parameter (shadow radius), the orbital frequency, a local acceleration scale, and eikonal quasinormal-mode damping. All principal inequalities reduce to the known four-dimensional results for $n=4$. Also, the bounds involving the critical impact parameter and orbital frequency are saturated by the Schwarzschild-Tangherlini vacuum solution. The results provide a compact set of consistency conditions linking the dimensionality of spacetime to the instability of photon trapping in Einstein gravity.
Comments10 pages, no figures
