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Kaluza-Klein Magnetized Cylindrical Wormhole and its Gravitational Lensing

A new exact vacuum solution in five dimensions, which describes a magnetized cylindrical wormhole in $3+1$ dimensions is presented. The magnetic field lines are stretched along the wormhole throat and are concentrated near to it. We study the motion of neutral and charged test particles under the influence of the magnetized wormhole. The effective potential for a neutral test particle around and across the magnetized wormhole has a repulsive character. The gravitational lensing for the magnetized wormhole for various lens parameters are calculated and compared. The total magnetic flux on either side of the wormhole is obtained. We present analytic expressions which show regions in which the null energy condition is violated.