论文标题
在黑洞和模糊黑影的边缘处的混乱
Chaos at the rim of black hole and fuzzball shadows
论文作者
论文摘要
我们研究了渐近探针在{\ it光子球}附近的无质量探针的散射，渐近地广告黑洞和无水平的微晶格几何（fuzzballs）。我们发现，这些表现出一种混乱的行为，其特征是附近轨迹的巨大偏差。我们计算了$ d $尺寸中的指数增长的lyapunov指数$λ$，并表明它以$λ_b= \ sqrt {d { - } 3}/2b _ {\ rm min} $ b _ {$ b _ {$ b _ {\ rm min taget tham tym tham int thame a get tramplublobluber是agt tham inmim tagpormorth或tham in a get tramp params a gets a a gets tramp parmate a n a n a n im imim tagemorth或在模糊中持续很长时间。此外，我们观察到$λ$通常低于混乱上的主张限制$λ_H=2πκ_Bt/\ hbar $，这反过来又表征了径向落入地平线，但在极端范围内违反了界限，在极端狭窄的窗口中，光子球形与地平线的光子相结合。最后，我们发现模糊球的特征是Lyapunov指数小于相应的BH的指数，这表明通过检测时间尺度的环形模式$λ^{ - 1} $比给定质量和旋转的BH的预期长期来区分地平线尺度上的微观结构的存在可能性。
We study the scattering of massless probes in the vicinity of the {\it photon-sphere} of asymptotically AdS black holes and horizon-free microstate geometries (fuzzballs). We find that these exhibit a chaotic behaviour characterised by exponentially large deviations of nearby trajectories. We compute the Lyapunov exponent $λ$ governing the exponential growth in $d$ dimensions and show that it is bounded from above by $λ_b = \sqrt{d{-}3}/2b_{\rm min}$ where $b_{\rm min}$ is the minimal impact parameter under which a massless particle is swallowed by the black hole or gets trapped in the fuzzball for a very long time. Moreover we observe that $λ$ is typically below the advocated bound on chaos $λ_H=2πκ_B T/\hbar$, that in turn characterises the radial fall into the horizon, but the bound is violated in a narrow window near extremality, where the photon-sphere coalesces with the horizon. Finally, we find that fuzzballs are characterised by Lyapunov exponents smaller than those of the corresponding BH's suggesting the possibility of discriminating the existence of micro-structures at horizon scales via the detection of ring-down modes with time scales $λ^{-1}$ longer than those expected for a BH of the given mass and spin.
