Causal concept for the general black hole shadow is investigated, instead of the photon sphere. We define several `wandering null geodesics' as complete null geodesics accompanied by repetitive conjugate points, which would correspond to null geodesics on the photon sphere in Schwarzschild spacetime. We also define a `wandering set', that is, a set of totally wandering null geodesics as a counterpart of the photon sphere, and moreover, a truncated wandering null geodesic to symbolically discuss its formation. Then we examine the existence of a wandering null geodesic in general black hole spacetimes mainly in terms of Weyl focusing. We will see the essence of the black hole shadow is not the stationary cycling of the photon orbits which is the concept only available in a stationary spacetime, but their accumulation. A wandering null geodesic implies that this accumulation will be occur somewhere in an asymptotically flat spacetime.

中文翻译：

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黑洞阴影的因果概念

研究了一般黑洞阴影的因果概念，而不是光子球。我们将几个“流浪零点测地线”定义为带有重复共轭点的完整零点测地线，这对应于 Schwarzschild 时空光子球上的零点测地线。我们还定义了一个“流浪集”，即一组完全流浪的零测地线作为光子球的对应物，此外，还定义了一个截断的流浪零测地线来象征性地讨论其形成。然后，我们主要根据外尔聚焦来研究一般黑洞时空中游荡零测地线的存在。我们将看到黑洞阴影的本质不是光子轨道的静止循环，这是一个仅在静止时空中可用的概念，而是它们的积累。