According to the no-hair theorem, astrophysical black holes are uniquely
described by their mass and spin. In this paper, we review a new framework for
testing the no-hair hypothesis with observations in the electromagnetic
spectrum. The approach is formulated in terms of a Kerr-like spacetime
containing a quadrupole moment that is independent of both mass and spin. If
the no-hair theorem is correct, then any deviation from the Kerr metric
quadrupole has to be zero. We show how upcoming VLBI imaging observations of
Sgr A* as well as spectroscopic observations of iron lines from accreting black
holes with IXO may lead to the first astrophysical test of the no-hair theorem.Comment: 5 pages, 3 figures, to appear in Adv. Space Res., Proc. COSPAR 201