The quantum fate of black hole horizons

TL;DR

This paper investigates how quantum effects alter the classical understanding of black hole horizons, showing that semiclassical geometries do not support traditional horizons and instead resemble tiny wormholes with exponentially small temperatures.

Contribution

It provides a non-perturbative analysis demonstrating that quantum effects prevent classical horizons, replacing them with wormhole-like structures and significantly reducing the temperature of large black holes.

Findings

Classical horizons are not solutions in semiclassical gravity.

Minimal 2-spheres are wormhole throats, not horizons.

Black hole temperature becomes exponentially small at large scales.

Abstract

The presence of a horizon is the principal marker for black holes as they appear in the classical theory of gravity. In General Relativity (GR), horizons have several defining properties. First, there exists a static spherically symmetric solution to vacuum Einstein equations which possesses a horizon defined as a null-surface on which the time-like Killing vector becomes null. Second, in GR, a co-dimension two sphere of minimal area is necessarily a horizon. On a quantum level, the classical gravitational action is supplemented by the quantum effective action obtained by integrating out the quantum fields propagating on a classical background. In this note we consider the case when the quantum fields are conformal and perform a certain non-perturbative analysis of the semiclassical equations obtained by varying the complete gravitational action. We show that, for these equations, both of the above aspects do not hold. More precisely, we prove that i) a static spherically symmetric metric that would describe a horizon with a finite Hawking temperature is, generically, {\it not} a solution; ii) a minimal $2$-sphere is {\it not} a horizon but a tiny throat of a wormhole. We find certain bounds on the norm of the Killing vector at the throat and show that it is, while non-zero, an exponentially small function of the Bekenstein-Hawking (BH) entropy of the classical black hole. We also find that the possible temperature of the semiclassical geometry is exponentially small for large black holes. These findings suggest that a black hole in the classical theory can be viewed as a certain (singular) limit of the semiclassical wormhole geometry. We discuss the possible implications of our results.