Note About Non-BPS and BPS Dp-branes in Near Horizon Region of N Dk-Branes

In this paper we will consider the dynamics of BPS and non-BPS Dp-branes in the background of N Dk-branes. Our approach is based on an existence of the new symmetry of D-brane effective actions that naturally emerges in the near horizon region of the stack of N Dk-branes. Since generally this scaling symmetry is explicitly broken in the Lagrangian we will find the equation that determines the time evolution of the generator of this transformations. Then we will argue that in case when the tachyon living on the worldvolume of unstable D-brane reaches the stable minimum the time evolution of this generator can be easily determined. With the help of the knowledge of the time dependence of this charge we will determine the trajectory of the non-BPS D-brane in the near horizon region of N Dk-branes. In case of BPS Dp-brane probe we will aruge that such a broken scaling symmetry exists as well and the existence of the explicit time dependence of the generator of this symmetry can be used in the solving the equation of motion of the probe Dp-brane in the near horizon region of N Dk-branes.