  Using ab initio calculations, we study the electronic and structural
properties of vacancies and hydrogen adsorbates on trilayer graphene. Those
defects are found to share similar low-energy electronic features, since they
both remove a pz electron from the honeycomb lattice and induce a defect level
near the Fermi energy. However, a vacancy also leaves unpaired $\sigma $
electrons on the lattice, which lead to important structural differences and
also contribute to magnetism. We explore both ABA and ABC stackings and compare
properties such as formation energies, magnetic moments, spin density and the
local density of states (LDOS) of the defect levels. These properties show a
strong sensitivity to the layer in which the defect is placed and smaller
sensitivities to sublattice placing and stacking type. Finally, for the ABC
trilayer, we also study how these states behave in the presence of an external
field, which opens a tunable gap in the band structure of the non-defective
system. The pz defect states show a strong hybridization with band states as
the field increases, with reduction and eventually loss of magnetization, and a
non-magnetic, midgap-like state is found when the defect is at the middle
layer.
