Vacuum polarization effects in the background of a deformed compact object and implications for photon velocity

TL;DR

This work investigates vacuum polarization effects on photon propagation in the spacetime of a distorted, deformed compact object described by a generalized $q$-metric with quadrupole parameters $\alpha$ (deformation) and $\beta$ (external distortion). Using a one-loop QED effective action in curved spacetime and the geometrical-optics limit, it derives polarization-dependent light-cone conditions that split into two eigenmodes (radial and transversal) and analyzes the resulting gravitational birefringence, including potential superluminal phase velocities while preserving causality in the group sense. The authors then study polarization-dependent gravitational lensing and shadows, deriving lens equations and light-ring conditions and applying the framework to Sagittarius A* to illustrate how $\alpha$ and $\beta$ shift the observed emission ring and shadow in a polarization-sensitive manner. Although the QED-induced effects are small (order $\xi^2$), they could become detectable with future high-precision observations, offering a novel test of quantum fields in curved spacetime and of the external quadrupole structure around compact objects.

Abstract

This paper studies the impact of vacuum polarization on light propagation in the background of a distorted, deformed compact object. Focusing on a spacetime containing two quadrupole parameters associated with the central object and external fields, we explore how these parameters influence observable effects as dynamical degrees of freedom. In this setup, we investigate electromagnetic birefringence, noting distinct polarization-dependent photon velocity variations and gravitational lens effects. Although current resolution may limit detection, future high-precision observations could reveal these quantum electrodynamics (QED) induced birefringence effects, advancing our understanding of vacuum birefringence in astrophysical contexts. We further analyze the dependence of shadow properties on the model's variables, using observational data from Sgr A*.

Figures (11)

• Figure 1: The photon velocity for the radial polarization equation and radial motion as a function of the distance $x$, for fixed parameters $M=1$ and $\xi=0.04$, and different values of the parameters $\alpha$ and $\beta$.
• Figure 2: The photon velocity for the radial polarization equation and orbital motion as a function of the distance $x$, for fixed parameters $M=1$ and $\xi=0.04$, and different values of the parameters $\alpha$ and $\beta$
• Figure 3: The photon velocity for the transversal polarization equation and radial motion as a function of the distance $x$, for fixed parameters $M=1$ and $\xi=0.04$, and for different values of the parameters $\alpha$ and $\beta$.
• Figure 4: The photon velocity for the transversal polarization equation and orbital motion as a function of the distance $x$, for fixed parameters $M=1$ and $\xi=0.04$, and for different values of the parameters $\alpha$ and $\beta$
• Figure 5: Lens diagram in the equatorial plane. The light ray of a source located at $(r_s,\phi_s)$, reaches the observer's position $(r_0,\phi_0=\pi)$ with incident angle $\Psi$, which determines the angular position of the image. Rays coming from the light ring have critical incident angle $\Psi_c$, and form the edge of the shadow. Only rays with $\Psi\geq\Psi_c$ can be observed. The distance to the point of closest approach is $r_p$.