Alberto Rubio-Ponce | Searcharxiv

arXiv2026

The G\"odel Universe as a Superconductor

Material science and engineering have benefited from the use of geometric and topological tools. A material medium can mimic effective gravitational fields while spacetime metrics serve as geometric models of physical media. Although analog models of optical, acoustic, and viscous media in curved spacetimes are well established, none have yet captured the hallmark constitutive properties of superconductors. In this work we show that the G\"odel universe - an exact solution to Einstein's field equations - serves as the gravitational analog of a superconducting medium in its Meissner state.

physics.gen-ph↗

arXiv2020

The geometry of induced electromagnetic fields in moving media

In this manuscript we provide a fully geometric formulation for the induced electromagnetic fields and their corresponding constitutive relations in moving media. To this end, we present the reader with a brief geometric summary to show how vector calculus electromagnetic theory is embedded in the more general language of differential forms. Then, we consider the class of \emph{metric} constitutive relations describing the medium in which electromagnetic fields propagate. We explicitly obtain the components of the induced fields in a moving medium, as seen in the the lab \emph{rest} frame. This allows us to read the expressions for the permitivity, permeability and magnetoelectric matrices for the moving medium which, in turn, can be interpreted as a different physical material from the lab point of view

physics.class-ph↗