Semiclassical black holes expose forbidden charges and censor divergent densities

TL;DR

This paper proposes a new approach to black hole physics by integrating out background fluctuations before matter observables, resolving issues like the information paradox and divergences at the horizon.

Contribution

It introduces a method to incorporate quantum background fluctuations in black hole models, revealing finite energy densities and measurable charges.

Findings

Average matter energy density is finite and proportional to BH entropy.

Global charges of black holes can, in principle, be measured.

The approach addresses the trans-Planckian problem and firewall controversy.

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.