Curved spacetime as a dispersive multiferroic medium for an electromagnetic wave: polarization and magnetization vectors in the Schwarzschild spacetime

TL;DR

This paper explores how electromagnetic waves behave in Schwarzschild spacetime, revealing that their properties resemble multiferroic materials near phase transitions, with susceptibilities linked to the Hawking temperature.

Contribution

It derives the electromagnetic wave equation in Schwarzschild spacetime and shows solutions in terms of confluent Heun functions, connecting gravitational effects to material-like electromagnetic properties.

Findings

Electromagnetic susceptibilities near the event horizon resemble those of multiferroic materials.

The behavior of susceptibilities indicates a phase transition at the Hawking temperature.

Solutions involve spherical harmonics and confluent Heun functions.

Abstract

We study one of the interesting properties of the electromagnetic wave propagation in the curved Schwarzschild background spacetime in the framework of general relativity (GR). The electromagnetic wave equation has been derived from vacuum general relativistic Maxwell's equations. It is shown that the solutions for the electromagnetic field can be expanded in the spherical harmonic functions and all components of the electromagnetic fields can be expressed in terms of two radial profile functions. These radial profile functions can be expressed in terms of the confluent Heun function. The calculated behaviour of the electric and magnetic susceptibilities near the event horizon appears to be similar to the susceptibilities of multiferroic materials near phase transition. The Curie temperature of this phase transition appears to coincide with the Hawking temperature.