  The super-massive objects at the center of many galaxies are commonly thought
to be black holes. In 4-dimensional general relativity, a black hole is
completely specified by its mass $M$ and by its spin angular momentum $J$. All
the higher multipole moments of the gravitational field depend in a very
specific way on these two parameters. For instance, the mass quadrupole moment
is $Q = - J^2/M$. If we can estimate $M$, $J$, and $Q$ for the super-massive
objects in galactic nuclei, we over-constrain the theory and we can test the
black hole hypothesis. While there are many works studying how this can be done
with future observations, in this paper a constraint on the quadrupole moment
of these objects is obtained by using the current estimate of the mean
radiative efficiency of AGN. In terms of the anomalous quadrupole moment $q$,
the bound is $-2.01 < q < 0.14$.
