The hidden horizon and black hole unitarity

TL;DR

This paper proposes a scheme consistent with quantum unitarity that describes black hole radiation without event horizons, suggesting the classical horizon is a coarse-grained, thermodynamic structure arising from quantum microstates.

Contribution

It introduces a novel framework where the classical event horizon emerges as a coarse-grained feature, maintaining unitarity and linking to microstate descriptions similar to fuzzballs.

Findings

Exclusive backgrounds prevent horizon formation due to Planckian fluctuations.

Inclusive backgrounds allow horizon formation as a coarse-grained structure.

Supports the thermodynamic interpretation of black hole entropy.

Abstract

We motivate through a detailed analysis of the Hawking radiation in a Schwarzschild background a scheme in accordance with quantum unitarity. In this scheme the semi-classical approximation of the unitary quantum - horizonless - black hole S-matrix leads to the conventional description of the Hawking radiation from a classical black hole endowed with an event horizon. Unitarity is borne out by the detailed exclusive S-matrix amplitudes. There, the fixing of generic out-states, in addition to the in-state, yields in asymptotic Minkowski space-time saddle-point contributions which are dominated by Planckian metric fluctuations when approaching the Schwarzschild radius. We argue that these prevent the corresponding macroscopic "exclusive backgrounds" to develop an event horizon. However, if no out-state is selected, a distinct saddle-point geometry can be defined, in which Planckian fluctuations are tamed. Such "inclusive background" presents an event horizon and constitutes a coarse-grained average over the aforementioned exclusive ones. The classical event horizon appears as a coarse-grained structure, sustaining the thermodynamic significance of the Bekenstein-Hawking entropy. This is reminiscent of the tentative fuzzball description of extremal black holes: the role of microstates is played here by a complete set of out-states. Although the computations of unitary amplitudes would require a detailed theory of quantum gravity, the proposed scheme itself, which appeals to the metric description of gravity only in the vicinity of stationary points, does not.