# Geometrization of gravito-electromagnetic interactions from boundary conditions in the variational principle

## TL;DR

This paper investigates how boundary conditions influence the geometric formulation of gravito-electromagnetic interactions, leading to emergent dynamics in extended manifolds with non-metricity, bridging gravity and electromagnetism.

## Contribution

It introduces a novel approach to derive gravito-electromagnetic interactions from boundary conditions in the variational principle within extended manifolds.

## Key findings

- Emergence of classical electrodynamics in extended manifolds
- Non-perturbative gravitational waves modeled in the framework
- Boundary conditions crucial for integrability and dynamics

## Abstract

We study the conditions of integrability when the boundary terms are considered in the variation of the geometric contribution of the Einstein-Hilbert action. We explore the emergent physical dynamics that is obtained when we make a displacement from a background Riemann manifold to an extended one, on which the non-metricity is nonzero. Under these circumstances, a classical description of electrodynamics and non-perturbative gravitational waves are considered in the extended manifold, when we variate the action.