Hawking radiation in quantum Hall system with an expanding edge: application of anomaly method

TL;DR

This paper demonstrates how gravitational anomaly methods can be applied to simulate Hawking radiation in a quantum Hall system with an expanding edge, revealing boundary effects analogous to de Sitter spacetime.

Contribution

It extends the anomaly method to a chiral quantum Hall system with an expanding edge, showing boundary effects induce Hawking radiation flux without needing ingoing mode conditions.

Findings

Hawking radiation flux matches Gibbons-Hawking temperature

Anomaly effects manifest as boundary conditions between regions

Method applicable to chiral quantum Hall systems

Abstract

The relationship between gravitational anomalies and Hawking radiation of black holes was revealed by Wilczek and Robinson. In this study, we apply their method to an analogue de Sitter spacetime in the quantum Hall system with an expanding edge. Because this system is chiral, there is no need to impose the condition of ingoing modes near the horizon, which was assumed in the original method. Moreover, this system is structured so that the de Sitter space is sandwiched between two flat spaces, and although the effects of the anomaly would not appear in an ordinal de Sitter spacetime, they manifest themselves as boundary conditions between the de Sitter and the flat regions. By performing calculations under these boundary conditions, we obtain the flux of Hawking radiation in the outer flat region with the Gibbons-Hawking temperature of the de Sitter horizon.