Semiclassical black holes expose forbidden charges and censor divergent densities

TL;DR

This work argues that classical black hole horizons cannot be treated as fixed, infinite-redshift surfaces in a semiclassical setting. By modeling the BH background as a fluctuating quantum object with a Gaussian wavefunction and integrating out these fluctuations before evaluating matter observables, the authors derive finite, power-law corrections in the horizon-classicality parameter $C_{BH}=1/S_{BH}$ and show that quantities like the near-horizon energy density scale as $1/C_{BH}$. The approach is illustrated through harmonic-oscillator analogies that reveal how strong background fluctuations regularize both vanishing and divergent interactions, and is then applied to classical and quantum fields near the BH horizon, yielding nonzero horizon currents and finite energy densities even in semiclassical regimes. The results offer a coherent resolution to several longstanding BH puzzles, including the possibility of measuring global charges, the taming of trans-Planckian divergences, and a way to address firewall concerns, while emphasizing that macroscopic BHs exhibit only small but finite corrections governed by $C_{BH}$.

Abstract

Classically, the black hole (BH) horizon is a rigid surface of infinite redshift; whereas the uncertainty principle dictates that the semiclassical (would-be) horizon cannot be fixed in space nor can it exhibit any divergences. We propose that this distinction underlies the BH information-loss paradox, the apparent absence of BH hair, the so-called trans-Planckian problem and the recent "firewall" controversy. We argue that the correct prescription is to first integrate out the fluctuations of the background geometry and only then evaluate matter observables. The basic idea is illustrated using a system of two strongly coupled harmonic oscillators, with the heavier oscillator representing the background. We then apply our proposal to matter fields near a BH horizon, initially treating the matter fields as classical and the background as semiclassical. In this case, the average value of the associated current does not vanish; so that it is possible, in principle, to measure the global charge of the BH. Then the matter is, in addition to the background, treated quantum mechanically. We show that the average energy density of matter as seen by an asymptotic observer is finite and proportional to the BH entropy, rather than divergent. We discuss the implications of our results for the various controversial issues concerning BH physics.