Black hole evaporation: A paradigm

TL;DR

The paper addresses black hole information loss within a non-perturbative quantum gravity framework. It combines loop quantum gravity's resolution of the Schwarzschild singularity with the dynamical-horizon formalism to develop a Lorentzian space-time picture of evaporation. The central claim is that quantum geometry resolves the singularity, leading to a non-singular interior and a single asymptotic region, so pure states can evolve to pure states on ${\mathscr{I}}^+$, thereby recovering information. The authors illustrate the paradigm with a qualitative four-dimensional scenario and draw on the CGHS model as a concrete analogue, outlining steps needed to extend to full 4D calculations. If validated, this framework could reconcile Hawking radiation with unitary quantum evolution and guide future quantum gravity and black hole thermodynamics research.

Abstract

A paradigm describing black hole evaporation in non-perturbative quantum gravity is developed by combining two sets of detailed results: i) resolution of the Schwarzschild singularity using quantum geometry methods; and ii) time-evolution of black holes in the trapping and dynamical horizon frameworks. Quantum geometry effects introduce a major modification in the traditional space-time diagram of black hole evaporation, providing a possible mechanism for recovery of information that is classically lost in the process of black hole formation. The paradigm is developed directly in the Lorentzian regime and necessary conditions for its viability are discussed. If these conditions are met, much of the tension between expectations based on space-time geometry and structure of quantum theory would be resolved.

Figures (4)

• Figure 1: The standard space-time diagram depicting black hole formation and evaporation.
• Figure 2: Space-time diagram of black hole evaporation where the classical singularity is resolved by quantum geometry effects. The shaded region lies in the 'deep Planck regime' where geometry is genuinely quantum mechanical. $H$ is the trapping horizon which is first space-like (i.e., a dynamical horizon) and grows because of infalling matter and then becomes time-like (i.e., a time-like membrane) and shrinks because of Hawking evaporation. In region I, there is a well-defined semi-classical geometry.
• Figure 3: The solid line with an arrow represents the world-line of an observer restricted to lie in region I. While these observers must eventually accelerate to reach ${\mathscr{I}}^+$, if they are sufficiently far away, they can move along an asymptotic time translation for a long time. The dotted continuation of the world line represents an observer who is not restricted to lie in region I. These observers can follow an asymptotic time translation all the way to $i^+$.
• Figure 4: The 'would be' space-time if the black hole were to take an infinite time to evaporate.