For an effective field theory in the background of an evaporating black hole with spherical symmetry, we consider non-renormalizable interactions and their relevance to physical effects. The background geometry is determined by the semi-classical Einstein equation for an uneventful horizon where the vacuum energy–momentum tensor is small for freely falling observers. Surprisingly, after Hawking radiation appears, the transition amplitude from the Unruh vacuum to certain multi-particle states grows exponentially with time for a class of higher-derivative operators after the collapsing matter enters the near-horizon region, despite the absence of large curvature invariants. Within the scrambling time, the uneventful horizon transitions towards a firewall, and eventually the effective field theory breaks down.

中文翻译：

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来自有效场理论的防火墙

对于具有球对称性的蒸发黑洞背景下的有效场论，我们考虑了不可重整化的相互作用及其与物理效应的相关性。背景几何由半经典爱因斯坦方程确定，其中真空能量-动量张量对于自由落体的观察者来说很小。令人惊讶的是，在霍金辐射出现后，尽管没有大曲率不变量，但在坍缩物质进入近视距区域后，一类高导数算子从安鲁真空到某些多粒子态的跃迁幅度随时间呈指数增长. 在打乱的时间内，平静的地平线过渡到防火墙，最终有效场论崩溃了。