Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that

TL;DR

This paper explores how curved graphene can simulate various quantum field theories in curved spacetimes, revealing new insights into Hawking radiation, spacetime geometries, and potential cosmological applications, with detailed geometric and physical analyses.

Contribution

It introduces a comprehensive framework for modeling quantum fields in curved graphene spacetimes, including new results on Hawking effect and spacetime geometries like de Sitter and BTZ black holes.

Findings

Reproduction of Rindler spacetime with key differences

Emergence of de Sitter spacetime in graphene models

Enhanced expression for thermal local density of states

Abstract

The solutions of many issues, of the ongoing efforts to make deformed graphene a tabletop quantum field theory in curved spacetimes, are presented. A detailed explanation of the special features of curved spacetimes, originating from embedding portions of the Lobachevsky plane into $\mathbf{R}^3$, is given, and the special role of coordinates for the physical realizations in graphene, is explicitly shown, in general, and for various examples. The Rindler spacetime is reobtained, with new important differences with respect to earlier results. The de Sitter spacetime naturally emerges, for the first time, paving the way to future applications in cosmology. The role of the BTZ black hole is also briefly addressed. The singular boundary of the pseudospheres, "Hilbert horizon", is seen to be closely related to event horizon of the Rindler, de Sitter, and BTZ kind. This gives new, and stronger, arguments for the Hawking phenomenon to take place. An important geometric parameter, $c$, overlooked in earlier work, takes here its place for physical applications, and it is shown to be related to graphene's lattice spacing, $\ell$. It is shown that all surfaces of constant negative curvature, ${\cal K} = -r^{-2}$, are unified, in the limit $c/r \to 0$, where they are locally applicable to the Beltrami pseudosphere. This, and $c = \ell$, allow us a) to have a phenomenological control on the reaching of the horizon; b) to use spacetimes different than Rindler for the Hawking phenomenon; c) to approach the generic surface of the family. An improved expression for the thermal LDOS is obtained. A non-thermal term for the total LDOS is found. It takes into account: a) the peculiarities of the graphene-based Rindler spacetime; b) the finiteness of a laboratory surface; c) the optimal use of the Minkowski quantum vacuum, through the choice of this Minkowski-static boundary.