Propagation of vacuum polarized photons in topological black hole spacetimes

TL;DR

This paper studies how vacuum polarized photons propagate in topological black hole spacetimes, revealing polarization-dependent velocity shifts influenced by spacetime topology and radiation, with implications for quantum field effects in curved spacetime.

Contribution

It extends the analysis of photon propagation and birefringence effects to topological black hole backgrounds, including radiating cases, highlighting the role of topology and radiation.

Findings

Photon velocity shifts depend on spacetime topology.

In static topological black holes, shifts match Reissner-Nordström case.

In radiating black holes, shifts occur even for radial photons.

Abstract

The one-loop effective action for QED in curved spacetime contains equivalence principle violating interactions between the electromagnetic field and the spacetime curvature. These interactions lead to the dependence of photon velocity on the motion and polarization directions. In this paper we investigate the gravitational analogue to the electromagnetic birefringence phenomenon in the static and radiating topological black hole backgrounds, respectively. For the static topological black hole spacetimes, the velocity shift of photons is the same as the one in the Reissner-Nordstr\"om black holes. This reflects that the propagation of vacuum polarized photons is not sensitive to the asymptotic behavior and topological structure of spacetimes. For the massless topological black hole and BTZ black hole, the light cone condition keeps unchanged. In the radiating topological black hole backgrounds, the light cone condition is changed even for the radially directed photons. The velocity shifts depend on the topological structures. Due to the null fluid, the velocity shift of photons does no longer vanish at the apparent horizons as well as the event horizons. But the ``polarization sum rule'' is still valid.