Lattice Black Holes

TL;DR

This paper investigates how Hawking radiation can emerge on a lattice with a short-distance cutoff, showing that under certain conditions the continuum Hawking spectrum is recovered despite the lattice structure.

Contribution

It demonstrates that Hawking radiation can be reproduced on a lattice with a cutoff, analyzing the effects of lattice symmetry and proper spacing on mode propagation.

Findings

Continuum Hawking spectrum is recovered for specific frequency conditions.

Outgoing modes originate from exotic ingoing modes with large wavevectors.

Time translation symmetry affects the transmutation of modes at the horizon.

Abstract

We study the Hawking process on lattices falling into static black holes. The motivation is to understand how the outgoing modes and Hawking radiation can arise in a setting with a strict short distance cutoff in the free-fall frame. We employ two-dimensional free scalar field theory. For a falling lattice with a discrete time-translation symmetry we use analytical methods to establish that, for Killing frequency $\omega$ and surface gravity $\kappa$ satisfying $\kappa\ll\omega^{1/3}\ll 1$ in lattice units, the continuum Hawking spectrum is recovered. The low frequency outgoing modes arise from exotic ingoing modes with large proper wavevectors that "refract" off the horizon. In this model with time translation symmetry the proper lattice spacing goes to zero at spatial infinity. We also consider instead falling lattices whose proper lattice spacing is constant at infinity and therefore grows with time at any finite radius. This violation of time translation symmetry is visible only at wavelengths comparable to the lattice spacing, and it is responsible for transmuting ingoing high Killing frequency modes into low frequency outgoing modes.