Towards a unitary formulation of quantum field theory in curved space-time: the case of Schwarzschild black hole

TL;DR

This paper introduces a novel quantum field theory framework in curved space-time, specifically for Schwarzschild black holes, aiming to resolve unitarity violations and information loss paradoxes by incorporating quantum effects and a direct-sum formalism.

Contribution

It proposes a direct-sum quantum field theory in black hole space-time that restores unitarity and avoids firewalls by accounting for quantum gravitational backreaction effects.

Findings

Hawking quanta inside and outside the horizon are correlated.

Black hole evaporation can be described as a pure state evolution.

The framework suggests a way to formulate a scattering matrix in quantum gravity.

Abstract

We argue that the origin of unitarity violation and information loss paradox in our understanding of black holes (BH) lies in the standard way of doing quantum field theory in curved space-time (QFTCS), which is heavily biased on intuition borrowed from classical General Relativity. In this paper, with the quantum first approach, we formulate a so-called direct-sum QFT (DQFT) in BH space-time based on a novel formulation of discrete space-time transformations in gravity that potentially restores unitarity. By invoking the quantum effects associated with the gravitational backreaction, we show that the Hawking quanta emerging outside of the Schwarzschild radius ($r_S=2GM$) cannot be independent of the quanta that continue to be inside $r_S$. This enables the information to be carried by Hawking quanta, but in the BH DQFT formalism, we do not get any firewalls. Furthermore, DQFT leads to the BH evaporation involving only pure states. This means the quantum mechanical effects at the BH horizon produce two components of a maximally entangled pure state in geometric superselection sector Hilbert spaces. This construction enables pure states to evolve into pure states, restoring unitarity and observer complementarity. Finally, we discuss how our framework leaves important clues for formulating a scattering matrix and probing the nature of quantum gravity.