Black-hole spectroscopy, the no-hair theorem, and GW150914: Kerr versus Occam

Juan Calderón Bustillo, Paul D. Lasky, Eric Thrane

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37 Citations (Scopus)


The "no-hair" theorem states that astrophysical black holes are fully characterized by just two numbers: their mass and spin. The gravitational-wave emission from a perturbed black-hole consists of a superposition of damped sinusoids, known as quasinormal modes. Quasinormal modes are specified by three integers (m,n): the (m) integers describe the angular properties and (n) specifies the (over)tone. If the no-hair theorem holds, the frequencies and damping times of quasinormal modes are determined uniquely by the mass and spin of the black hole, while phases and amplitudes depend on the particular perturbation. Current tests of the no-hair theorem attempt to identify these modes in a semiagnostic way, without imposing priors on the source of the perturbation. This is usually known as black-hole spectroscopy. Applying this framework to GW150914, the measurement of the first overtone led to the confirmation of the theorem to 20% level. We show, however, that such semiagnostic tests cannot provide strong evidence in favor of the no-hair theorem, even for extremely loud signals, given the increasing number of overtones (and free parameters) needed to fit the data. This can be solved by imposing prior assumptions on the origin of the perturbed black hole that can further constrain the explored parameters: in particular, our knowledge that the ringdown is sourced by a binary black-hole merger. Applying this strategy to GW150914, we find a natural log Bayes factor of ∼6.5 in favor of the Kerr nature of its remnant, indicating that the hairy object hypothesis is disfavored with <1:600 with respect to the Kerr black-hole one.

Original languageEnglish
Article number024041
Number of pages12
JournalPhysical Review D
Issue number2
Publication statusPublished - 15 Jan 2021

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