On Nanocones as a Gravitational Analog System

TL;DR

This paper investigates the torsional energy properties of nanocones in graphene and boron nitride, validating TEGR's predictions through simulations and proposing a method to estimate its coupling constant, linking material physics with gravitational theory.

Contribution

It provides the first quantitative analysis of TEGR's energy expression in nanostructures, connecting microscopic interatomic forces to gravitational concepts.

Findings

Torsional energy depends linearly on disclination angle.

Simulation results align with TEGR's theoretical predictions.

Estimated coupling constant $k$ relates to interatomic forces.

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.