Raychaudhuri equation in quantum gravitational optics

N AHMADI¹ and M NOURI-ZONOZ^1,2

¹Department of Physics, University of Tehran, North Karegar Ave., Tehran 14395-547, Iran

²Institute for Studies in Theoretical Physics and Mathematics,

P.O. Box 19395-5531 Tehran, Iran

E-mail: nahmadi@ut.ac.ir; nouri@theory.ipm.ac.ir

Abstract. The equation of Raychaudhuri is one of the key concepts in

the formulation of the singularity theorems introduced by Penrose and

Hawking. In the present article, taking into account QED vacuum

polarization, we study the propagation of a bundle of rays in a

background gravitational field through the perturbative deformation of

Raychaudhuri's equation. In a sense, this could be seen as another

semiclassical study in which geometry is treated classically but

matter (which means the photon here) is allowed to exhibit quantum

characteristics that are encoded in its coupling to the background

curvature.

Keywords. Raychaudhuri equation; quantum gravitational optics;

vacuum polarization.

PACS No. 04.62.+v