The Effect of Gravitational Tidal Forces on Vacuum Polarization: How to Undress a Photon

Abstract

The effect of gravitational tidal forces on photon propagation in curved spacetime is investigated. It is found that the imaginary part of the local refractive index Im n(u;w) may be negative as well as positive, corresponding to a local amplification as well as attenuation of the amplitude of the renormalized photon field. This is interpreted in terms of the effect of tidal forces on the virtual e^+e^- cloud surrounding the bare photon field---a positive/negative Im n(u;w) corresponds to an increased dressing/undressing of the bare photon. Below threshold decays of the photon to e^+e^- pairs can occur. Photon undressing in the vicinity of a black hole singularity is described as an example. These results are shown to be consistent with unitarity and the optical theorem in curved spacetime, which is derived here both in a local form and integrated over the photon trajectory.

Figures (1)

• Figure 1: Diagrams which illustrate the the cases where the photon amplitude decreases (top) and increases (bottom) arising from the production of more/less virtual $e^+ e^-$ pairs, respectively. The top/bottom cases occurs when the rate of change of the acceleration on nearby geodesics is positive/negative.