Semi-classical probe strings on giant gravitons backgrounds

In the first part of this paper we study two $Z_2$ symmetries of the LLMmetric, both of which exchange black and white regions. One of them which canbe interpreted as the particle-hole symmetry is the symmetry of the wholesupergravity solution while the second one is just the symmetry of the metricand changes the sign of the fivefrom flux. In the second part of the paper weuse closed string probes and their semi-classical analysis to compare the two1/2 BPS deformations of $AdS_5\times S^5$, the smooth LLM geometry whichcontains localized giant gravitons and the superstar case which is a solutionwith naked singularity corresponding to smeared giants. We discuss therealization of the $Z_2$ symmetry in the semi-classical closed string probespoint of view.Comment: 29 pages, 6 .eps figures; v2: References adde