Hollow cosmic string: The general-relativistic hollow cylinder

Abstract

We determine the different possible space-time metrics inside an infinite rotating hollow cylinder with a given energy density and longitudinal and azimuthal stresses, the metric outside the cylinder being chosen of the spinning cosmic string type. The solutions we obtain for various domains of values of the cylinder parameters include a space-time with topologically Euclidean spatial sections, a black-hole solution, a quasiregular solution, and various wormhole solutions. A solution which is regular only if the longitudinal dimension is compactified might approximately describe spontaneous compactification of the cylinder to a torus.

Static cylindrical matter shells

“…These solutions correspond to a cosmic string shell and in the first one the interior region is flat [5,17]. Same results are also presented in [11].…”

“…Actually, it is known [5]- [8], [11] that the matching conditions yield the conditions for the shell to be matter shell or shell composed of massless particles. The shells composed of photons is studied recently in detail.…”

Multiwormholes and multi-black-holes in three dimensions

“…with Y periodic, may similarly arise as an interior solution generated by an infinite cylinder of exotic matter, leading to a black cosmic string [8].…”

Wormhole cosmic strings

“…For the special value κν 2 = 2, Kaluza-Klein cosmic string space-times with negative deficit angle may also be derived from our σ-model wormhole space-times. Making for five-dimensional general relativity with three commuting Killing vectors the ansatz [13,8] 4,5) where φ varies on the unit sphere (φ 2 = 1), we reduce the five-dimensional Einstein-Hilbert action to…”