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Register a new userBlack-hole spectroscopy, the no-hair theorem and GW150914: Kerr vs. Occam
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Added by
Juan Calderon Bustillo
Publication date
2020
fields
Physics
and research's language is
English
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The no-hair theorem states that astrophysical black holes are fully characterised 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 textit{quasi-normal modes}. Quasi-normal modes are specified by three integers $(ell,m,n)$: the $(ell, m)$ integers describe the angular properties and $(n)$ specifies the (over)tone. If the no-hair theorem holds, the frequencies and damping times of quasi-normal 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 semi-agnostic way, without imposing priors on the source of the perturbation. This is usually known as textit{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 semi-agnostic tests cannot provide strong evidence in favour 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 $sim 6.5$ in favour of the Kerr nature of its remnant, indicating that the hairy object hypothesis is disfavoured with $<1:600$ with respect to the Kerr black-hole one.
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Validating the black-hole no-hair theorem with gravitational-wave observations of compact binary coalescences provides a compelling argument that the remnant object is indeed a black hole as described by the general theory of relativity. This requires performing a spectroscopic analysis of the post-merger signal and resolving the frequencies of either different angular modes or overtones (of the same angular mode). For a nearly-equal mass binary black-hole system, only the dominant angular mode ($l=m=2$) is sufficiently excited and the overtones are instrumental to perform this test. Here we investigate the robustness of modelling the post-merger signal of a binary black hole coalescence as a superposition of overtones. Further, we study the bias expected in the recovered frequencies as a function of the start time of a spectroscopic analysis and provide a computationally cheap procedure to choose it based on the interplay between the expected statistical error due to the detector noise and the systematic errors due to waveform modelling. Moreover, since the overtone frequencies are closely spaced, we find that resolving the overtones is particularly challenging and requires a loud ringdown signal. Rayleighs resolvability criterion suggests that in an optimistic scenario a ringdown signal-to-noise ratio larger than $sim 30$ (achievable possibly with LIGO at design sensitivity and routinely with future interferometers such as Einstein Telescope, Cosmic Explorer, and LISA) is necessary to resolve the overtone frequencies. We then conclude by discussing some conceptual issues associated with black-hole spectroscopy with overtones.
We analyze gravitational-wave data from the first LIGO detection of a binary black-hole merger (GW150914) in search of the ringdown of the remnant black hole. Using observations beginning at the peak of the signal, we find evidence of the fundamental quasinormal mode and at least one overtone, both associated with the dominant angular mode ($ell=m=2$), with $3.6sigma$ confidence. A ringdown model including overtones allows us to measure the final mass and spin magnitude of the remnant exclusively from postinspiral data, obtaining an estimate in agreement with the values inferred from the full signal. The mass and spin values we measure from the ringdown agree with those obtained using solely the fundamental mode at a later time, but have smaller uncertainties. Agreement between the postinspiral measurements of mass and spin and those using the full waveform supports the hypothesis that the GW150914 merger produced a Kerr black hole, as predicted by general relativity, and provides a test of the no-hair theorem at the ${sim}10%$ level. An independent measurement of the frequency of the first overtone yields agreement with the no-hair hypothesis at the ${sim 20}%$ level. As the detector sensitivity improves and the detected population of black hole mergers grows, we can expect that using overtones will provide even stronger tests.
Bopp-Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekensteins method. It is shown the solutions split-up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp-Podolsky black holes, the non-homogeneous solutions are found to be Maxwells solutions leading to a Reissner-Nordstrom black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwells one. Thus, in light of energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp-Podolsky fields in spherically symmetric space-times.
Gravitational waves provide a window to probe general relativity (GR) under extreme conditions. The recent observations of GW190412 and GW190814 are unique high-mass-ratio mergers that enable the observation of gravitational-wave harmonics beyond the dominant $(ell, m) = (2, 2)$ mode. Using these events, we search for physics beyond GR by allowing the source parameters measured from the sub-dominant harmonics to deviate from that of the dominant mode. All results are consistent with GR. We constrain the chirp mass as measured by the $(ell, m) = (3, 3)$ mode to be within $0_{-3}^{+5}%$ of the dominant mode when we allow both the masses and spins of the sub-dominant modes to deviate. If we allow only the mass parameters to deviate, we constrain the chirp mass of the $(3, 3)$ mode to be within $pm1%$ of the expected value from GR.
We study a hairy black hole solution in the dilatonic Einstein-Gauss-Bonnet theory of gravitation, in which the Gauss-Bonnet term is non-minimally coupled to the dilaton field. Hairy black holes with spherical symmetry seem to be easily constructed with a positive Gauss-Bonnet coefficient $alpha$ within the coupling function, $f(phi) = alpha e^{gamma phi}$, in an asymptotically flat spacetime, i.e., no-hair theorem seems to be easily evaded in this theory. Therefore, it is natural to ask whether this construction can be expanded into the case with the negative coefficient $alpha$. In this paper, we present numerically the dilaton black hole solutions with a negative $alpha$ and analyze the properties of GB term through the aspects of the black hole mass. We construct the new integral constraint allowing the existence of the hairy solutions with the negative $alpha$. Through this procedure, we expand the evasion of the no-hair theorem for hairy black hole solutions.
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