BPS Mass, Dirichlet Boundary Condition, and the Isotropic Coordinate System

We consider test strings and test branes ending on D$p$-branes ($p\le 6$) and NS5-branes in the background, for a heuristic understanding of the dynamics. Whenever some supersymmetry is preserved, a simple BPS bound appears, but the central charge in question is measured by certain isotropic coordinate system, rather than by the actual spacetime geometry. This way, the ground state energy is independent of the gravitational radii of the solitonic background. Furthermore, a perturbation around the supersymmetric ground states reveals that the appropriate Dirichlet boundary condition is dynamically induced. We close with comments.