# The gravitational magnetoelectric effect

## TL;DR

This paper explores the gravitational analogue of the linear magnetoelectric effect, demonstrating its dependence on formalism choices and coordinate systems in various spacetime metrics.

## Contribution

It reveals how the gravitational magnetoelectric effect varies with formalism and coordinate choices, extending understanding of electromagnetism in curved spacetime.

## Key findings

- Effect depends on tensor formalism and coordinate chart choices.
- Illustrated in Schwarzschild and pp wave spacetimes.
- Shows variability of the effect with different formalisms.

## Abstract

Electromagnetism in spacetime can be treated in terms of an analogue linear dielectric medium. In this paper, we discuss the gravitational analogue of the linear magnetoelectric effect, which can be found in multiferroic materials. While this is known to occur for metrics with non-zero mixed components, we show how it depends on the choice of spatial formalism for the electromagnetic fields, including in differences in tensor weight, and also on the choice of coordinate chart. This is illustrated for Langevin-Minkowski, four charts of Schwarzschild spacetime, and two charts of pp gravitational waves.