On graviton-photon conversions in magnetic environments

TL;DR

This paper examines graviton-photon conversions in magnetic fields, emphasizing the importance of correctly identifying electromagnetic fields in curved spacetime and revealing potential tachyonic instabilities caused by magnetic environments.

Contribution

It clarifies the proper treatment of EM fields in curved spacetime for graviton-photon conversion and introduces the impact of magnetic environments on gravitational wave stability.

Findings

Correct identification of EM fields is crucial in curved spacetime.

Magnetic environments can induce tachyonic instabilities in gravitational waves.

Proper metric inclusion alters the graviton-photon conversion equations.

Abstract

Graviton-photon conversions in a given external electric or magnetic field, known as the Gertsenshtein mechanism, are usually treated using the four-potential for photons. In terms of the electric and magnetic (EM) fields, however, proper identification of the fields in curved spacetime is important. By misidentifying the fields in Minkowski form, as is often practiced in the literature, we show that the final equation for photon conversion is correct in transverse-tracefree gauge only for planar gravitational waves in a uniform and constant external field. Even in the former method, to recover the EM fields from the four-potential in curved spacetime, one should properly take into account the metric involved in the relation. By including the metric perturbation in the graviton conversion equation, we show that a magnetic environment can cause tachyonic instability term in gravitational wave equation.