  We study physical properties of constant curvature black holes (CCBHs) in
Einstein anti-de Sitter (AdS) gravity. These objects, which are locally AdS
throughout the space, are constructed from identifications of global AdS
spacetime, in a similar fashion as Banados-Teitelboim-Zanelli (BTZ) black hole
in three dimensions. We find that, in dimensions equal or greater than four,
CCBHs have zero mass and angular momentum. Only in odd dimensions we are able
to associate a nonvanishing conserved quantity to these solutions, which
corresponds to the vacuum (Casimir) energy of the spacetime.
