论文标题
五维几何形状的光环
Light rings of five-dimensional geometries
论文作者
论文摘要
我们在五个维度上研究了爱因斯坦 - 马克斯韦理论的大型解决方案的光子范围内的无质量测量学，包括BHS，裸体奇异性和平滑地平线的JMART几何形状，这些几何形状是五维解决方案的六维升高。我们发现，质量中心周围不稳定的光子轨道的光环总是存在的，独立于地平线或奇异性的存在。我们计算了Lyapunov指数，表征了“光子 - 球”附近的混乱行为，以及降落模式的时间衰减，占主导地位的几何响应对几何对扰动的响应。我们表明，对于没有裸露奇点的几何形状，Lyapunov指数始终受其对同一质量的Schwarzschild BH的价值的界限。
We study massless geodesics near the photon-spheres of a large family of solutions of Einstein-Maxwell theory in five dimensions, including BHs, naked singularities and smooth horizon-less JMaRT geometries obtained as six-dimensional uplifts of the five-dimensional solution. We find that a light ring of unstable photon orbits surrounding the mass center is always present, independently of the existence of a horizon or singularity. We compute the Lyapunov exponent, characterizing the chaotic behaviour of geodesics near the `photon-sphere' and the time decay of ring-down modes dominating the response of the geometry to perturbations at late times. We show that, for geometries free of naked singularities, the Lyapunov exponent is always bounded by its value for a Schwarzschild BH of the same mass.
