D-brane orbiting NS5-branes

We study real time dynamics of a Dp-brane orbiting a stack of NS5-branes. It is generally known that a BPS D-brane moving in the vicinity of NS5-branes becomes unstable due to the presence of tachyonic degree of freedom induced on the D-brane. Indeed, the D-brane necessarily falls into the fivebranes due to gravitational attraction and eventually collapses into a pressureless fluid. Such a decay of the D-brane is known to be closely related to the rolling tachyon problem. In this paper we show that in special cases the decay of D-brane caused by gravitational attraction can be avoided. Namely for certain values of energy and angular momentum the D-brane orbits around the fivebranes, maintaining certain distance from the fivebranes all the time, and the process of tachyon condensation is suppressed. We show that the tachyonic degree of freedom induced on such a D-brane really disappears and the brane returns to a stable D-brane.