The information loss paradox

TL;DR

This thesis investigates the black hole information loss paradox by deriving quantum field theory results in curved spacetime, analyzing Hawking radiation, and exploring recent developments in asymptotic symmetries and soft hair.

Contribution

It provides a detailed derivation of Hawking radiation and discusses the role of asymptotic symmetries and soft hair in the context of the information paradox.

Findings

Hawking radiation temperature derived from QFT in curved spacetime

Black hole states remain mixed at first order with small quantum corrections

Recent links between gravitational memory, supertransformations, and soft hair are discussed

Abstract

In this thesis, we have studied the information loss paradox in detail. As a first step, we have derived the main results of quantum field theory in a curved background. We have discussed the case of the free scalar Klein-Gordon field and concluded with a derivation of the so-called Unruh effect in Minkowski spacetime. After giving a brief survey of necessary concepts, such as surface gravity and the redshift factor, we have applied them along the results from the Unruh effect to derive the temperature of Hawking radiation. Later, we have used the formalism of QFT in curved spacetime to rigorously obtain the distribution of the radiation, considering a black hole formation process. Thus, we have focused on the quantum mechanical states of the radiation quanta and the mass in the black hole, showing that at first order plus small corrections (condition needed to neglect effects of quantum gravity in normal physics) the Hawking conclusion of mixed states/remnants holds. Finally, we have presented some of the principal results of the recent study of asymptotic symmetries and the $BMS_4$ symmetry group. We have concluded presenting some ideas relating the gravitational memory effect with the supertransformations and the soft hair carrying the black holes.