Constraint on the quadrupole moment of super-massive black hole candidates from the estimate of the mean radiative efficiency of AGN

The supermassive 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 supermassive objects in galactic nuclei, we overconstrain 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.