Abstract
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.
Highlights
We show that there are higher-dimensional interactions with large physical effects in the near-horizon region where the curvature is small, and that this eventually leads to the formation of a firewall and the breakdown of the effective field theory within the time scale of the so-called “scrambling time” [24]
We showed that Hawking radiation is incompatible with the uneventful horizon
Unruh vacuum in the near-horizon region of the dynamical black hole so that it evolves into an excited state with many high-energy particles for freely falling observers
Summary
The information hidden inside a nucleus in free fall cannot be retrieved unless there are events (e.g., scatterings) above the scale of the QCD binding energy3 This conflict between an uneventful horizon and unitarity has been emphasized in Refs. We show that there are higher-dimensional interactions with large physical effects in the near-horizon region where the curvature is small, and that this eventually leads to the formation of a firewall and the breakdown of the effective field theory within the time scale of the so-called “scrambling time” [24].
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