On the cylindrically symmetric wormholes WhCR^e: The motion of test particles

TL;DR

This paper investigates the motion of test particles in cylindrically symmetric wormholes within a 6-dimensional Kaluza-Klein framework, analyzing their trajectories and traversability akin to black hole geometries.

Contribution

It extends previous work by studying non-radial particle motion in cylindrically symmetric wormholes, identifying critical impact parameters and orbit types affecting traversability.

Findings

Identifies critical impact parameter D_c separating different orbit types.

Classifies orbits into three categories based on impact parameter and stability.

Shows wormhole traversability depends on particle impact parameters.

Abstract

In this article we partially implement the program outlined in the previous paper of the authors [A. V. Aminova and P. I. Chumarov, Phys. Rev. D 88, 044005 (2013)]. The program owes its origins to the following comment in paper [M. Cveti\v{c} and D. Youm, Nucl. Phys. B, 438, 182 (1995), Addendum-ibid. 449,146 (1995)], where a class of static spherically symmetric solutions in $(4+n)$-dimensional Kaluza--Klein theory was studied: "...We suspect that the same thing [as for spherical symmetry] will happen for axially symmetric stationary configurations, but it remains to be proven". We study the radial and non-radial motion of test particles in the cylindrically symmetric wormholes found in the authors'paper of type $\rm WhCR^e$ in 6-dimensional reduced Kaluza--Klein theory with Abelian gauge field and two dilaton fields, with particular attention to the extent to which the wormhole is traversable. In the case of non-radial motion along a hypersurface z=const we show that, as in the Kerr and Schwarzschild geometries, we should distinguish between orbits with impact parameters greater resp. less than a certain critical value $D_c$, which corresponds to the unstable circular orbit of radius $u_c$ $(r_c)$. For $D^2>D_c^2$ there are two kinds of orbits: orbits of the first kind arrive from infinity and have pericenter distances greater than $u_c$, whereas orbits of the second kind have apocenter distances less than $u_c$ and terminate at the singularity at $u=-\infty$ $(r=0)$. For $D=D_c$ orbits of the first and second kinds merge and both orbits spiral an infinite number of times toward the unstable circular orbit $u=u_c$. For $D^2<D_c^2$ we have only orbits of one kind: starting at infinity, they cross the wormhole throat and terminate at the singularity.