2015/11/24 by Simone Taioli, Ruggero Gabbrielli, Taioli, Simone +7
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Materials Science (cond-mat.mtrl-sci) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1511.07672
openalex publication_date 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We realize Lobachevsky geometry in a simulation lab, by producing a carbon-based mechanically stable molecular structure, arranged in the shape of a Beltrami pseudosphere. We find that this structure: i) corresponds to a non-Euclidean crystallographic group, namely a loxodromic subgroup of SL(2,Z); ii) has an unavoidable singular boundary, that we fully take into account. Our approach, substantiated by extensive numerical simulations of Beltrami pseudospheres of different size, might be applied to other surfaces of constant negative Gaussian curvature, and points to a general procedure to generate them. Our results also pave the way to test certain scenarios of the physics of curved spacetimes.