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 .