On Nanocones as a Gravitational Analog System

Abstract

This study delves into the fundamental properties of graphene and boron nitride (BN) nanostructures, exploring their torsional energy characteristics within the framework of Teleparallel Equivalent of General Relativity (TEGR). By constructing nanocones with disclination defects in these materials, we investigate the linear dependence of torsional energy on the disclination angle, as predicted by TEGR. The qualitative validation of TEGR's energy expression is supported by our simulations, which show a strong correlation between the torsional energy and the disclination angle, consistent with the theoretical predictions. Furthermore, we propose a quantitative analysis by estimating the coupling constant $k$ associated with TEGR through molecular simulations and Density Functional Theory (DFT) calculations. Our results suggest that $k$ reflects the interatomic forces within the materials, providing insights into the nature of spacetime and gravitational interactions on a microscopic scale. These findings not only contribute to our understanding of material physics but also offer implications for the precision and validity of TEGR in describing gravitational phenomena.

14 pages, 7 figures. Sections revised and new figure added

References in corpus (14)

• Graphene: Status and Prospects
• Mechanical Properties of Atomically Thin Boron Nitride and the Role of Interlayer Interactions
• The teleparallel equivalent of general relativity
• Geometric Theory of Defects
• Geodesics around line defects in elastic solids
• Has Hawking radiation been measured?
• Space-time defects and teleparallelism
• Current density and conductivity through modified gravity in the graphene with defects
• Disclinations in the geometric theory of defects
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• Point disclinations in the Chern-Simons geometric theory of defects
• Torsional Elastic Waves in Cylindrical Waveguide with Wedge Dislocation
• On the Quantization of Burgers Vector and Gravitational Energy in the Space-Time of a Conical Defect
• A robophysical model of spacetime dynamics

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