Predictability and Semiclassical Approximation at the onset of Black Hole formation

TL;DR

This paper investigates the collapse of scalar fields near black hole formation in 2D semiclassical gravity, revealing how information recovery becomes harder near criticality and how unitarity breaks down at the threshold.

Contribution

It combines analytical and numerical methods to analyze the transition from classical to quantum regimes during black hole formation, highlighting the limits of semiclassical approximation.

Findings

Information recovery from outgoing radiation becomes more difficult near criticality.

Outgoing quantum radiation includes both Hawking radiation and a negative-energy flux for energy conservation.

Unitarity breaks down at the critical solution, linked to semiclassical approximation failure.

Abstract

We combine analytical and numerical techniques to study the collapse of conformally coupled massless scalar fields in semiclassical 2D dilaton gravity, with emphasis on solutions just below criticality when a black hole almost forms. We study classical information and quantum correlations. We show explicitly how recovery of information encoded in the classical initial data from the outgoing classical radiation becomes more difficult as criticality is approached. The outgoing quantum radiation consists of a positive-energy flux, which is essentially the standard Hawking radiation, followed by a negative-energy flux which ensures energy conservation and guarantees unitary evolution through strong correlations with the positive-energy Hawking radiation. As one reaches the critical solution there is a breakdown of unitarity. We show that this breakdown of predictability is intimately related to a breakdown of the semiclassical approximation.