A quantum scalar field inside the horizon of a non-rotating BTZ black hole is studied. Not only the near-horizon modes but also the normal modes deep inside the horizon are obtained. It is shown that the matching condition for the normal modes of a scalar field at the horizon does not uniquely determine the normal-mode expansion of a scalar field inside the horizon. By choosing a certain appropriate prescription for removing this ambiguity an integral form of a new scalar propagator for points on both sides of the horizon are obtained. A similar problem may arise in higher-dimensional black holes.

中文翻译：

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BTZ 黑洞视界内部

研究了非旋转 BTZ 黑洞视界内的量子标量场。不仅可以获得近地平线模式，还可以获得地平线深处的正常模式。结果表明，视界内标量场的常模的匹配条件并不能唯一地决定视界内标量场的常模扩展。通过选择某种适当的方法来消除这种歧义，就可以得到一个新的标量传播器的积分形式，用于地平线两侧的点。在更高维的黑洞中可能会出现类似的问题。