General relativity predicts that a black hole that results from the merger of two compact stars (either black holes or neutron stars) is initially highly deformed but soon settles down to a quiescent state by emitting a superposition of quasi-normal modes (QNMs). The QNMs are damped sinusoids with characteristic frequencies and decay times that depend only on the mass and spin of the black hole and no other parameter - a statement of the no-hair theorem. In this paper we have examined the extent to which QNMs could be used to test the no-hair theorem with future ground- and space-based gravitational-wave detectors. We model departures from general relativity (GR) by introducing extra parameters which change the mode frequencies or decay times from their general relativistic values. With the aid of numerical simulations and Bayesian model selection, we assess the extent to which the presence of such a parameter could be inferred, and its value estimated. We find that it is harder to decipher the departure of decay times from their GR value than it is with the mode frequencies. Einstein Telescope (ET, a third generation ground-based detector) could detect departures of <1% in the frequency of the dominant QNM mode of a 500 Msun black hole, out to a maximum range of 4 Gpc. In contrast, the New Gravitational Observatory (NGO, an ESA space mission to detect gravitational waves) can detect departures of ~ 0.1% in a 10^8 Msun black hole to a luminosity distance of 30 Gpc (z = 3.5).
We study the capability of the space-based gravitational wave observatory TianQin to test the no-hair theorem of General Relativity, using the ringdown signal from the coalescence of massive black hole binaries. We parameterize the ringdown signal by the four strongest quasinormal modes and estimate the signal to noise ratio for various source parameters. We consider constraints both from single detections and from all the events combined throughout the lifetime of the observatory, for different astrophysical models. We find that at the end of the mission, TianQin will have constrained deviati…
The Einstein Telescope (ET), a proposed third-generation gravitational wave observatory, would enable tests of the no-hair theorem by looking at the characteristic frequencies and damping times of black hole ringdown signals. In previous work it was shown that with a single $500 - 1000\,M_\odot$ black hole at distance $\lesssim 6$ Gpc (or redshift $z \lesssim 1$), deviations of a few percent in the frequencies and damping times of dominant and sub-dominant modes would be within the range of detectability. Given that such sources may be relatively rare, it is of interest to see how well the no-…
We show that second-generation gravitational-wave detectors at their design sensitivity will allow us to directly probe the ringdown phase of binary black hole coalescences. This opens the possibility to test the so-called black hole no-hair conjecture in a statistically rigorous way. Using state-of-the-art numerical relativity-tuned waveform models and dedicated methods to effectively isolate the quasi-stationary perturbative regime where a ringdown description is valid, we demonstrate the capability of measuring the physical parameters of the remnant black hole, and subsequently determining …
The ringdown is the late part of the post-merger signature emitted during the coalescence of two black holes and comprises of a superposition of quasi-normal-modes. Within general relativity, because of the no-hair theorems, the frequencies and damping times of these modes are entirely determined by the mass and angular momentum of the final Kerr black hole. A detection of multiple ringdown modes would potentially allow us to test the no-hair theorem from observational data. The parameters which determine whether sub-dominant ringdown modes can be detected are primarily the overall signal-to-n…
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 i…
General relativity's no-hair theorem states that isolated astrophysical black holes are described by only two numbers: mass and spin. As a consequence, there are strict relationships between the frequency and damping time of the different modes of a perturbed Kerr black hole. Testing the no-hair theorem has been a longstanding goal of gravitational-wave astronomy. The recent detection of gravitational waves from black hole mergers would seem to make such tests imminent. We investigate how constraints on black hole ringdown parameters scale with the loudness of the ringdown signal---subject to …
General relativity admits a plethora of exact compact object solutions. The augmentation of Einstein's action with non-minimal coupling terms leads to modified theories with rich structure, which, in turn, provide non-trivial solutions with intriguing phenomenology. Thus, assessing their viability under generic fluctuations is of utmost importance for gravity theories. We consider static and spherically-symmetric solutions of a Horndeski subclass which includes a massless scalar field non-minimally coupled to the Einstein tensor. Such theory possesses second-order field equations and admits an…
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 $3.6σ$ 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 sig…
Exceptional Points in Quasinormal Spectra of Hairy Black Holes
College of Physics, Sichuan University（四川大学物理学院）；School of Data Science, Shanghai University of Finance and Economics Zhejiang College（上海财经大学浙江学院数据科学学院）
The direct discovery of gravitational waves from compact binary systems leads for the first time to explore the possibility of black hole spectroscopy. Newly formed black holes produced by coalescing events are copious emitters of gravitational radiation, in the form of damped sinusoids, the quasi normal modes. The latter provide a precious source of information on the nature of gravity in the strong field regime, as they represent a powerful tool to investigate the validity of the no-hair theorem. In this work we perform a systematic study on the accuracy with which current and future interfe…
The black hole uniqueness and the no-hair theorems imply that the quasinormal spectrum of any astrophysical black hole is determined solely by its mass and spin. The countably infinite number of quasinormal modes of a Kerr black hole are thus related to each other and any deviations from these relations provide a strong hint for physics beyond the general theory of relativity. To test the no-hair theorem using ringdown signals, it is necessary to detect at least two quasinormal modes. In particular, one can detect the fundamental mode along with a subdominant overtone or with another angular m…
It is possible to infer the mass and spin of the remnant black hole from binary black hole mergers by comparing the ringdown gravitational wave signal to results from studies of perturbed Kerr spacetimes. Typically these studies are based on the fundamental quasinormal mode of the dominant $\ell=m=2$ harmonic. By modeling the ringdown of accurate numerical relativity simulations, we find that the fundamental mode alone is insufficient to recover the true underlying mass and spin, unless the analysis is started very late in the ringdown. Including higher overtones associated with this $\ell=m=2…
For a distorted black hole (BH), its ringdown waveform is a superposition of quasi-normal modes (QNMs). In general relativity (GR), the lower order QNM frequencies and damping rates can be well approximated by a polynomial of BH's dimensionless spin and overall scaled by BH's mass. That is to say, we can test the no-hair theorem of BH in GR model-independently by allowing not only an overall fractional deviation (as M. Isi {\it et al.} did) but also a set of fractional deviation for every coefficient. In the paper, we will apply the latter method to retest the no-hair theorem with GW150914 and…
The behavior of hairy black hole solutions, obtained by the gravitational decoupling (GD) method, is investigated under scalar perturbations. The quasinormal mode frequencies of such solutions are regulated by GD hair. The numerically generated wave solutions are derived for a range of values for the GD hairy black hole parameters, with higher-frequency modes very sensitive to them. The results are confronted with the corresponding ones for the Schwarzschild solution, whose deviations from it demonstrate a unique physical identification of GD hairy black holes. The method here presented compri…
A perturbed black hole rings down by emitting gravitational waves in tones with specific frequencies and durations. Such tones encode prized information about the geometry of the source spacetime and the fundamental nature of gravity, making the measurement of black hole ringdowns a key goal of gravitational wave astronomy. However, this task is plagued by technical challenges that invalidate the naive application of standard data analysis methods and complicate sensitivity projections. In this paper, we provide a comprehensive account of the formalism required to properly carry out ringdown a…
We perform an observational test of no-hair theorem using quasi-periodic oscillations within the relativistic precession model. Two well motivated metrics we apply are Kerr-Q and Hartle-Thorne metrics in which the quadrupole is the parameter that possibly encodes deviations from the Kerr black hole. The expressions for the quasi-periodic frequencies are derived before comparing the models with the observation. We encounter a degeneracy in constraining spin and quadrupole parameters that makes it difficult to measure their values. In particular, we here propose a novel test of no-hair theorem b…
The no-hair conjecture in General Relativity (GR) states that a Kerr black hole (BH) is completely described by its mass and spin. As a consequence, the complex quasi-normal-mode (QNM) frequencies of a binary-black-hole (BBH) ringdown can be uniquely determined by the mass and spin of the remnant object. Conversely, measurement of the QNM frequencies could be an independent test of the no-hair conjecture. This paper extends to spinning BHs earlier work that proposed to test the no-hair conjecture by measuring the complex QNM frequencies of a BBH ringdown using parameterized inspiral-merger-rin…
The final ringdown phase in a coalescence process is a valuable laboratory to test General Relativity and potentially constrain additional degrees of freedom in the gravitational sector. We introduce here an effective description for perturbations around spherically symmetric spacetimes in the context of scalar-tensor theories, which we apply to study quasi-normal modes for black holes with scalar hair. We derive the equations of motion governing the dynamics of both the polar and the axial modes in terms of the coefficients of the effective theory. Assuming the deviation of the background fro…
The continuum-fitting and the iron line methods are leading techniques capable of probing the spacetime geometry around astrophysical black hole candidates and testing the no-hair theorem. In the present paper, we review the two approaches, from the astrophysical models and their assumptions, to the constraining power with present and future facilities.
Gravitational wave observations of the ringdown of the remnant black hole in a binary black hole coalescence provide a unique opportunity of confronting the black hole no-hair theorem in general relativity with observational data. The most robust tests are possible if multiple ringdown modes can be observed. In this paper, using state-of-the-art Bayesian inference methods and the most up-to-date knowledge of binary black hole population parameters and ringdown mode amplitudes, we evaluate the prospects for black hole spectroscopy with current and future ground based gravitational wave detector…
Advanced LIGO's recent observations of gravitational waves (GWs) from merging binary black holes have opened up a unique laboratory to test general relativity (GR) in the highly relativistic regime. One of the tests used to establish the consistency of the first LIGO event with a binary black hole merger predicted by GR was the inspiral-merger-ringdown consistency test. This involves inferring the mass and spin of the remnant black hole from the inspiral (low-frequency) part of the observed signal and checking for the consistency of the inferred parameters with the same estimated from the post…
Echoes of a hairy black hole from gravitational decoupling
Guizhou University of Finance and Economics（贵州财经大学）；Eastern Mediterranean University（东地中海大学）；Universit degli Studi di Salerno（萨莱诺大学）；Istituto Nazionale di Fisica Nucleare - Gruppo Collegato di Salerno - Sezione di Napoli（意大利国家核物理研究所 - 萨莱诺协作组 - 那不勒斯分部）；Guizhou Minzu University（贵州民族大学）；Guizhou University（贵州大学）
Black holes in General Relativity are very simple objects. This property, that goes under the name of "no-hair," has been refined in the last few decades and admits several versions. The simplicity of black holes makes them ideal testbeds of fundamental physics and of General Relativity itself. Here we discuss the no-hair property of black holes, how it can be measured in the electromagnetic or gravitational window, and what it can possibly tell us about our universe.
Gravitational-wave (GW) observations of binary black holes offer the best probes of the relativistic, strong-field regime of gravity. Gravitational radiation, in the leading order is quadrupolar. However, non-quadrupole (higher-order) modes make appreciable contribution to the radiation from binary black holes with large mass ratios and misaligned spins. The multipolar structure of the radiation is fully determined by the intrinsic parameters (masses and spin angular momenta of the companion black holes) of a binary in quasi-circular orbit. Following our previous work \cite{Dhanpal:2018ufk}, w…
Quasinormal Modes and Hawking Radiation of Black Holes with Primary Scalar Hair
Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理研究所理论物理与天体物理研究中心）；Institute of Cosmology, Department of Physics and Astronomy, Tufts University（塔夫茨大学物理与天文学系宇宙学研究所）；Institute of Physics in Opava, Silesian University in Opava（奥帕瓦西里西亚大学奥帕瓦物理研究所）
The ringdown part of gravitational waves in the final stage of merger of compact objects tells us the nature of strong gravity which can be used for testing the theories of gravity. The ringdown waveform, however, fades out in a very short time with a few cycles, and hence it is challenging for gravitational wave data analysis to extract the ringdown frequency and its damping time scale. We here propose to build up a suite of mock data of gravitational waves to compare the performance of various approaches developed to detect quasi-normal modes from a black hole. In this paper we present our i…
We present observational confirmation of Hawking's black-hole area theorem based on data from GW150914, finding agreement with the prediction with 97% (95%) probability when we model the ringdown including (excluding) overtones of the quadrupolar mode. We obtain this result from a new time-domain analysis of the pre- and postmerger data. We also confirm that the inspiral and ringdown portions of the signal are consistent with the same remnant mass and spin, in agreement with general relativity.
In light of the current (and future) gravitational wave detections, more sensitive tests of general relativity can be devised. Black hole spectroscopy has long been proposed as a way to test the no-hair theorem, that is, how closely an astrophysical black hole can be described by the Kerr geometry. We use simulations from the Simulating eXtreme Spacetimes project to assess the detectability of one extra quasinormal mode in the ringdown of a binary black hole coalescence, with numbers $(\ell,m,n)$ distinct from the fundamental quadrupolar mode (2,2,0). Our approach uses the complex waveform as …
Gravitational waves are rapidly becoming a very reliable tool for testing alternative theories of gravity. In particular, features in the gravitational wave emission during black hole ringdown phase provide a direct probe of the spacetime outside the black hole. In this article, we consider black holes in ghost-free massive gravity. These black holes generically have scalar hair. We found that a simple coupling between gravitational perturbations and this scalar hair can change the quasinormal ringing of the black hole, and in particular, produce echoes in the emitted gravitational waves. This…
Quasi-normal modes (QNMs) of a black hole (BH) are the eigen modes describing the dissipative oscillation of various fields in that spacetime, which can be intrinsically produced by the linear perturbation theory. With the discovery of the first gravitational waves (GWs) event, GW150914, a new window into the universe has been opened, allowing for the detection of QNMs associated to the ringdown process, which will enable more accurate measurements of the BHs parameters as well as further testing of general relativity. This article discusses the linear perturbation theory of BHs and provides r…
