Decoherence of Black Holes by Hawking Radiation

TL;DR

This paper analyzes the semiclassical approximation of two-dimensional black holes, demonstrating how Hawking radiation emerges and can cause decoherence of black hole superpositions, advancing understanding of quantum effects in black hole physics.

Contribution

It provides a detailed semiclassical analysis of the CGHS black hole model, explicitly deriving Hawking radiation and exploring its role in decoherence of black hole superpositions.

Findings

Hawking radiation exhibits a Planckian distribution at the Hawking temperature.

Decoherence of black hole superpositions can be caused by Hawking radiation.

Explicit treatment of superpositions of black holes with white holes or no holes.

Abstract

We discuss in detail the semiclassical approximation for the CGHS model of two-dimensional dilatonic black holes. This is achieved by a formal expansion of the full Wheeler-DeWitt equation and the momentum constraint in powers of the gravitational constant. In highest order, the classical CGHS solution is recovered. The next order yields a functional Schr\"odinger equation for quantum fields propagating on this background. We show explicitly how the Hawking radiation is recovered from this equation. Although described by a pure quantum state, the expectation value of the number operator exhibits a Planckian distribution with respect to the Hawking temperature. We then show how this Hawking radiation can lead to the decoherence of black hole superpositions. The cases of a superposition of a black hole with a white hole, as well as of a black hole with no hole, are treated explicitly.