On Nanocones as Gravitational Analog Systems

This study investigates 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, the linear dependence of torsional energy on the disclination angle is analyzed, as predicted by TEGR. The qualitative validation of TEGR's energy expression is supported by simulations, which show a strong correlation between torsional energy and the disclination angle, consistent with theoretical predictions. Additionally, a quantitative analysis is proposed by estimating the coupling constant $\kappa$ associated with TEGR through molecular simulations and Density Functional Theory (DFT) calculations. The results suggest that $\kappa$ reflects the interatomic forces within the materials, providing insights into the nature of spacetime and gravitational interactions on a microscopic scale. These findings contribute to the understanding of material physics and offer implications for the precision and validity of TEGR in describing gravitational phenomena.