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

摘要

The solutions of many issues, of the ongoing efforts to make deformed graphene a tabletop\udquantum field theory in curved spacetimes, are presented. A detailed explanation of the special\udfeatures of curved spacetimes, originating from embedding portions of the Lobachevsky plane into\udR3, is given, and the special role of coordinates for the physical realizations in graphene is explicitly\udshown, in general, and for various examples. The Rindler spacetime is reobtained, with new\udimportant differences with respect to earlier results. The de Sitter spacetime naturally emerges, for the\udfirst time, paving the way to future applications in cosmology. The role of the Bañados, Teitelboim,\udand Zanelli (BTZ) black hole is also briefly addressed. The singular boundary of the pseudospheres,\ud“Hilbert horizon,” is seen to be closely related to the event horizon of the Rindler, de Sitter, and BTZ\udkind. This gives new, and stronger, arguments for the Hawking phenomenon to take place. An\udimportant geometric parameter, c, overlooked in earlier work, takes here its place for physical\udapplications, and it is shown to be related to graphene’s lattice spacing, l. It is shown that all surfaces\udof constant negative curvature, K ¼ −r−2, are unified, in the limit c=r → 0, where they are locally\udapplicable to the Beltrami pseudosphere. This, and c ¼ l, allow us (a) to have a phenomenological\udcontrol on the reaching of the horizon; (b) to use spacetimes different from the Rindler spacetime for\udthe Hawking phenomenon; and (c) to approach the generic surface of the family. An improved\udexpression for the thermal LDOS is obtained. A nonthermal term for the total LDOS is found. It takes\udinto account (i) the peculiarities of the graphene-based Rindler spacetime; (ii) the finiteness of a\udlaboratory surface; and (iii) the optimal use of the Minkowski quantum vacuum, through the choice\udof this Minkowski-static boundary.