Letter: Multiple Photonic Shells Around a Line Singularity

Abstract

Line singularities including cosmic strings may be screened by photonic shells until they appear as a planar wall.KEY WORDS: Levi-Civita spacetime, photonic shells.Infinitely thin static photonic shells composed of equal amounts of oppositely moving photons following circular, helical or axial trajectories around a cosmic string [1] and, around a general line singularity [2] have recently been found. In this paper, we will find solutions giving multiple photonic shells around a line singularity. Multiple photonic shells around cosmic strings will be obtained as a limiting case. We will show that the exterior region of the (multiple) shells may become an infinite plane wall.The vacuum spacetime exterior to a static, cylindrically symmetric source is described by the Levi-Civita metric [3] which can be written as:where t , ρ, z and φ are the time, the radial, the axial and the angular variables of the cylindrical coordinates with ranges −∞ < t, z < ∞, 0 ≤ ρ < ∞ and 0 ≤ φ ≤ 2π. σ, P and Q are real constants. Transforming the radius ρ into a proper radius r by defining dr = ρ 2σ(2σ−1) dρ puts (1) in the Kasner form:

Comments on photonic shells

“…Since they have constant coordinate velocities, their trajectories are necessarily circular geodesics within the 3-dimensional subspace of the cylindrical shell. A similar situation with multiple photonic shells has been discussed recently in [7] (the authors use the Kasner form of the metric ‡)-we focus on a special case of a single shell formed by non-helical photons with flat regions both inside and outside.…”