Gravitational instantons as models for charged particle systems

TL;DR

This paper models charged particle systems using ALF gravitational instantons of types A_k and D_k, calculating their charges and constructing energy functionals that replicate Coulomb interactions.

Contribution

It introduces gravitational instantons as models for charged particles and develops energy functionals based on topological structures to simulate Coulomb interactions.

Findings

Charges of A_k and D_k instantons are calculated.

Energy functionals reproduce Coulomb interaction energies.

Models can represent electrons, protons, and their combinations.

Abstract

In this paper we propose ALF gravitational instantons of types A_k and D_k as models for charged particle systems. We calculate the charges of the two families. These are -(k +1) for A_k, which is proposed as a model for k+1 electrons, and 2-k for D_k, which is proposed as a model for either a particle of charge +2 and k electrons or a proton and k-1 electrons. Making use of preferred topological and metrical structures of the manifolds, namely metrically preferred representatives of middle dimension homology classes, we construct two different energy functionals which reproduce the Coulomb interaction energy for a system of charged particles.