Quantum gravitational optics: Effective Raychaudhuri equation

Vacuum polarization in QED in a background gravitational field induces interactions which effectively modify the classical picture of light rays, as the null geodesics of spacetime. These interactions violate the strong equivalence principle and affect the propagation of light leading to superluminal photon velocities. Taking into account the QED vacuum polarization, we study the propagation of a bundle of rays in a background gravitational field. To do so we study the perturbative deformation of the Raychaudhuri equation through the influence of vacuum polarization on photon propagation. We analyze the contribution of the above interactions to the optical scalars, namely, shear, vorticity, and expansion using the Newman-Penrose formalism.

Figure 1

Three abreast rays of a congruence and the small triangle formed by two connecting vectors ${\xi }_1$ and ${\xi }_2$, connecting the ray $\gamma$ to the rays ${\gamma }_1$ and ${\gamma }_2$ in the $m\overline{m}$-plane.