Cosmic expansion influences the angular size of black hole shadow. The most general way to describe a black hole embedded into an expanding universe is to use the McVittie metric. So far, the exact analytical solution for the shadow size in the McVittie metric, valid for arbitrary law of expansion and arbitrary position of the observer, has not been found. In this paper, we present the first analytical solution for angular size of black hole shadow in McVittie metric as seen by observer comoving with the cosmic expansion. We use a method of matched asymptotic expansions to find approximate solution valid within the entire range of possible positions of observer. As two particular examples, we consider black hole in de Sitter and matter-dominated universe.

中文翻译：

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首次在 McVittie 度量中解析计算黑洞阴影

宇宙膨胀影响黑洞阴影的角度大小。描述嵌入膨胀宇宙的黑洞的最一般方法是使用 McVittie 度量。到目前为止，尚未找到适用于任意膨胀定律和观察者任意位置的 McVittie 度量中阴影大小的精确解析解。在本文中，我们提出了观察者看到的与宇宙膨胀共同移动的 McVittie 度量中黑洞阴影角大小的第一个解析解。我们使用匹配渐近展开的方法来找到在观察者可能位置的整个范围内有效的近似解。作为两个特定的例子，我们考虑德西特和物质主导的宇宙中的黑洞。