  In this paper the zero modes of the de Donder gauge Faddeev-Popov operator
for three dimensional gravity with negative cosmological constant are analyzed.
It is found that the three dimensional AdS vacuum produces (infinitely many)
normalizable, smooth zero modes of the Faddeev-Popov operator. On the other
hand, it is found that the BTZ black hole (including the zero mass black hole)
does not generate zero modes. This differs from the usual Gribov problem in QCD
where close to the maximally symmetric vacuum, the Faddeev-Popov determinant is
positive definite while "far enough" from the vacuum it can vanish. This
suggests that the zero mass BTZ black hole could be a suitable ground state of
three dimensional gravity with negative cosmological constant. Due to the
kinematic origin of this result, it also applies for other covariant gravity
theories in three dimensions with AdS_3 as maximally symmetric solution, such
as new massive gravity and topologically massive gravity. The relevance of
these results for SUSY breaking is pointed out.
