Geometrical tachyon kinks andNS5 branes

We further investigate the $NS$5 ring background using the tachyon map.Mapping the radion fields to the rolling tachyon helps to explain the motion ofa probe $Dp$-brane in this background. It turns out that the radion fieldbecomes tachyonic when the brane is confined to one dimensional motion insidethe ring. We find explicit solutions for the geometrical tachyon field thatdescribe stable kink solutions which are similar to those of the open stringtachyon. Interestingly in the case of the geometric tachyon, the dynamics iscontrolled by a cosine potential. In addition, we couple a constant electricfield to the probe-brane, but find that the only stable kink solutions occurwhen there is zero electric field or a critical field value. We alsoinvestigate the behaviour of Non-BPS branes in this background, and find thatthe end state of any probe brane is that of tachyonic matter 'trapped' aroundthe interior of the ring. We conclude by considering compactification of thering solution in one of the transverse directions.Comment: Latex, 24 pages, 1 eps fig; clarifying comments added to Section 2; typos correcte