The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes

TL;DR

This paper investigates how quantum loop effects influence light propagation in curved spacetime, extending previous scalar QED results to spinor QED, and explores implications for black holes, cosmology, and gravitational waves.

Contribution

It extends the calculation of the refractive index in curved spacetime from scalar to spinor QED, analyzing causality and potential instabilities in various gravitational backgrounds.

Findings

Low frequency phase velocity can exceed c without violating causality.

Refractive index behavior varies with spacetime geometry and polarization.

Potential optical theorem breakdown and instabilities in certain conditions.

Abstract

This work considers the way that quantum loop effects modify the propagation of light in curved space. The calculation of the refractive index for scalar QED is reviewed and then extended for the first time to QED with spinor particles in the loop. It is shown how, in both cases, the low frequency phase velocity can be greater than c, as found originally by Drummond and Hathrell, but causality is respected in the sense that retarded Green functions vanish outside the lightcone. A "phenomenology" of the refractive index is then presented for black holes, FRW universes and gravitational waves. In some cases, some of the polarization states propagate with a refractive index having a negative imaginary part indicating a potential breakdown of the optical theorem in curved space and possible instabilities.