  In the first part of this paper we study two $Z_2$ symmetries of the LLM
metric, both of which exchange black and white regions. One of them which can
be interpreted as the particle-hole symmetry is the symmetry of the whole
supergravity solution while the second one is just the symmetry of the metric
and changes the sign of the fivefrom flux. In the second part of the paper we
use closed string probes and their semi-classical analysis to compare the two
1/2 BPS deformations of $AdS_5\times S^5$, the smooth LLM geometry which
contains localized giant gravitons and the superstar case which is a solution
with naked singularity corresponding to smeared giants. We discuss the
realization of the $Z_2$ symmetry in the semi-classical closed string probes
point of view.
