Firewalls as artefacts of inconsistent truncations of quantum geometries

Abstract

In this paper we argue that a firewall is simply a manifestation of an inconsistent truncation of non-perturbative effects that unitarize the semiclassical black hole. Namely, we show that a naive truncation of quantum corrections to the Hawking spectrum at order $\mathcal{O}(e^{-S})$, inexorably leads to a "localised'' divergent energy density near the black hole horizon. Nevertheless, in the same approximation, a distant observer only sees a discretised spectrum and concludes that unitarity is achieved by $\mathcal{O}(e^{-S})$ effects. This is due to the fact that instead, the correct quantum corrections to the Hawking spectrum go like $\mathcal{O}(g^{tt}{e}^{-S})$. Therefore, while at a distance far away from the horizon, where $g^{tt}\approx 1$, quantum corrections {\it are} perturbative, they {\it do} diverge close to the horizon, where $g^{tt}\to \infty$. Nevertheless, these "corrections" nicely re-sum so that correlations functions are smooth at the would-be black hole horizon. Thus, we conclude that the appearance of firewalls is just a signal of the breaking of the semiclassical approximation at the Page time, even for large black holes.

v4: explanation about the failure of the saddle point approximation and general clarifications added

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