Hawking radiation on a falling lattice

TL;DR

This paper investigates Hawking radiation using a falling lattice model in 1+1 dimensions, demonstrating that the effect can be accurately simulated with a discretized scalar field theory through both analytical and numerical methods.

Contribution

It introduces a lattice falling into a black hole to model Hawking radiation, showing the effect arises from mode mixing analogous to Bloch oscillations, with high accuracy.

Findings

Hawking radiation is reproduced within 0.5% accuracy on a properly spaced lattice.

Outgoing modes originate from incoming modes via a process similar to Bloch oscillations.

Numerical results confirm the theoretical predictions of mode mixing and Hawking radiation emergence.

Abstract

Scalar field theory on a lattice falling freely into a 1+1 dimensional black hole is studied using both WKB and numerical approaches. The outgoing modes are shown to arise from incoming modes by a process analogous to a Bloch oscillation, with an admixture of negative frequency modes corresponding to the Hawking radiation. Numerical calculations show that the Hawking effect is reproduced to within 0.5% on a lattice whose proper spacing where the wavepacket turns around at the horizon is $\sim0.08$ in units where the surface gravity is 1.