# Premetric approach in gravity and electrodynamics

## TL;DR

This paper explores the premetric formalism in gravity and electrodynamics, showing how classical theories can be developed without relying on a metric, thus providing deeper insights into their foundational structures.

## Contribution

It demonstrates a premetric formulation of electrodynamics and offers new perspectives on the interplay between topological, affine, and metric aspects in relativistic gravity theories.

## Key findings

- Electrodynamics can be formulated without a metric.
- Premetric approach clarifies the relationship between topological and metric concepts.
- Provides a unified view of gravity and electromagnetism foundations.

## Abstract

The basics of the premetric approach are discussed, including the essential details of the formalism and some of its beautiful consequences. We demonstrate how the classical electrodynamics can be developed without a metric in a quite straightforward way: Maxwell's equations, together with the general response law for material media, admit a consistent premetric formulation. Furthermore, we show that in relativistic theories of gravity, the premetric program leads to a better understanding of the interdependence between topological, affine, and metric concepts.