Graviton-photon mixing. Exact solution in a constant magnetic field

Damian Ejlli

doi:10.1007/jhep06(2020)029

Abstract

In this work I study the effect of graviton-photon mixing in a constant external magnetic field and find for the first time in the literature exact solution of the equations of motion. In particular, I apply the effect of graviton-photon mixing to the case of interaction of gravitational waves with an external magnetic field and calculate the intensity Stokes parameter of the produced electromagnetic radiation. The obtained results are new and extend previous results obtained by using approximation methods.

Highlights

JHEP06(2020)029 features of the propagating GW were found due to the not use of gauge invariant methods since these studies did not make use of the TT-gauge to remove unphysical degrees of freedom in the specific case of graviton-photon mixing. The latter case was included in the study of ref. [7] where quantum field theory approach was used but no medium effects on the electromagnetic radiation were included
I address all the problems mentioned above and find for the first time in the literature exact solution of the equations of motion of graviton-photon mixing in a constant magnetic field and derive user friendly relations in the case when GWs are stochastic in nature
The results found in this work are new and improve previous results where approximate methods have been used to solve the equations of motion and possible medium effects on the electromagnetic waves were not included

Summary

Formulation of the problem

Since we consider the case when we are far away from the GW source(s), we can put GWs in the TT gauge before entering the magnetic field region, namely h0μ = 0, ∂jhij = 0, hii = 0 In this case the effective action becomes. With the GW and electromagnetic wave propagating along the zaxis, hij = hij(z, t), Ai = Ai(z, t) and with the field expansion (2.4), the equations of motion (2.3) for the GW tensor hij in terms of the GW polarization states h+ and h× are given by ω2 + ∂z2 h+(z, ω) = −κ ∂zAx(z, ω)By + ∂zAy(z, ω)Bx , ω2 + ∂z2 h×(z, ω) = κ ∂zAx(z, ω)Bx − ∂zAy(z, ω)By ,. The system (2.8) in order to be solved has to be supplied with appropriate initial conditions and/or boundary conditions if needed

Exact analytical solution of equations of motion

Energy flux and density parameter of generated electromagnetic radiation

Conclusions