Supermassive black holes or boson stars? Hair counting with gravitational wave detectors

The evidence for supermassive Kerr black holes in galactic centers is strong and growing, but only the detection of gravitational waves will convincingly rule out other possibilities to explain the observations. The Kerr spacetime is completely specified by the first two multipole moments: mass and angular momentum. This is usually referred to as the no-hair theorem'', but it is really a two-hair’’ theorem. If general relativity is the correct theory of gravity, the most plausible alternative to a supermassive Kerr black hole is a rotating boson star. Numerical calculations indicate that the spacetime of rotating boson stars is determined by the first three multipole moments (three-hair theorem''). LISA could accurately measure the oscillation frequencies of these supermassive objects. We propose to use these measurements to count their hair’', unambiguously determining their nature and properties.