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.
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…
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…
In this note an analytic integration is obtained for the differential equation governing the scalar-field-dependent mass in a hairy binary black hole model, in the context of the Einstein--Maxwell--dilation theory, which gives a closed-form formula-level description of the mass function. We also identify a particular solution which attracts all solutions of the mass-governing equation exponentially rapidly in large-dilaton-field limit.
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 am…
One of the consequences of the black-hole "no-hair" theorem in general relativity (GR) is that gravitational radiation (quasi-normal modes) from a perturbed Kerr black hole is uniquely determined by its mass and spin. Thus, the spectrum of quasi-normal mode frequencies have to be all consistent with the same value of the mass and spin. Similarly, the gravitational radiation from a coalescing binary black hole system is uniquely determined by a small number of parameters (masses and spins of the black holes and orbital parameters). Thus, consistency between different spherical harmonic modes of…
We consider a binary system in the context of screened modified gravity models and investigate its emitted gravitational wave which has been shown that is a hairy wave. We derive power of the gravitational wave and the binding energy of the binary system and then trace back the effect of the additional scalar field, present at screening models, in the frequency of GW emitted from the binary. The binary is considered as two astrophysical black holes in a spherically symmetric galactic ambient/halo with constant density. Effectively in the ISCO region the screening force is in charge due to the …
Advanced LIGO's ability to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem through compact binary coalescence detections
We continue our study on the capabilities of present and future X-ray missions to test the nature of astrophysical black hole candidates via X-ray reflection spectroscopy and distinguish Kerr black holes from other solutions of 4-dimensional Einstein's gravity in the presence of a matter field. Here we investigate the case of Kerr black holes with Proca hair [1]. The analysis of a sample of these configurations suggests that even extremely hairy black holes can mimic the iron line profile of the standard Kerr black holes, and, at least for the configurations of our study, we find that current …
In General Relativity and many modified theories of gravity, isolated black holes (BHs) cannot source massless scalar fields. Einstein-Maxwell-dilaton (EMd) theory is an exception: through couplings both to electromagnetism and (non-minimally) to gravity, a massless scalar field can be generated by an electrically charged BH. In this work, we analytically model the dynamics of binaries comprised of such scalar-charged ("hairy") BHs. While BHs are not expected to have substantial electric charge within the Standard Model of particle physics, nearly-extremally charged BHs could occur in models o…
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…
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 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…
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…
We study the nonlinear dynamics of black holes that carry scalar hair and binaries composed of such black holes. The scalar hair is due to a linear or exponential coupling between the scalar and the Gauss--Bonnet invariant. We work perturbatively in the coupling constant of that interaction but nonperturbatively in the fields. We first consider the dynamical formation of hair for isolated black holes of arbitrary spin and determine the final state. This also allows us to compute for the first time the scalar quasinormal modes of rotating black holes in the presence of this coupling. We then st…
Gravitational Memory from Hairy Binary Black Hole Mergers
CERN（欧洲核子研究组织）；KU Leuven（荷语鲁汶大学）；Universitat de València（瓦伦西亚大学）；Eberhard Karls University of Tübingen（蒂宾根大学）；Sofia University “St. Kliment Ohridski”（索非亚大学）；Bulgarian Academy of Sciences（保加利亚科学院）
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…
Dynamical hair growth in black hole binaries in Einstein-scalar-Gauss-Bonnet gravity
SISSA（的里雅斯特国际高等研究学院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；Dipartimento di Fisica, Sapienza Università di Roma（罗马第一大学物理系）；Instituut voor Theoretische Fysica, KU Leuven（荷鲁芬大学理论物理研究所）；Leuven Gravity Institute, KU Leuven（荷鲁芬大学引力研究所）；Departament d’Astronomia i Astrofísica, Universitat de València（瓦伦西亚大学天文与天体物理学系）；Theoretical Astrophysics, Eberhard Karls University of Tübingen（蒂宾根大学理论天体物理学）；Department of Theoretical Physics, Faculty of Physics, Sofia University（索非亚大学物理学院理论物理系）；Institute of Mathematics and Informatics, Bulgarian Academy of Sciences（保加利亚科学院数学与信息学研究所）
We derive the energy fluxes radiated by compact binary systems, including "hairy" black holes, in Einstein-Maxwell-dilaton theories, for circular orbits and at quadrupolar order. This enables to include in their resummed effective-one-body (EOB) dynamics the effect of the radiation reaction force at the origin of their inspiral and merger. We also exhibit typical examples of the resulting tensor and scalar waveforms.
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 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…
As one of the consequences of the black-hole "no-hair" theorem in general relativity (GR), the multipolar structure of the radiation (i.e. different spherical harmonic modes) from a merging quasi-circular binary black hole (BBH) is fully determined by the intrinsic parameters (i.e. the masses and spins of the companion black holes). In Refs. [1,2], we have formulated an efficient test named `higher-modes consistency test' to check for the consistency of the observed gravitational-wave (GW) signal with the expected multipolar structure of radiation from BBHs in GR. Detection of the high-mass-ra…
Inspiral gravitational waveforms from charged compact binaries with scalar hair
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力波物理与量子信息研究中心）；Department of Physics, Waseda University（早稻田大学物理学部）
We propose a novel method to test the binary black hole (BBH) nature of compact binaries detectable by gravitational wave (GW) interferometers and hence constrain the parameter space of other exotic compact objects. The spirit of the test lies in the "no-hair" conjecture for black holes where all properties of a black hole are characterised by the mass and the spin of the black hole. The method relies on observationally measuring the quadrupole moments of the compact binary constituents induced due to their spins. If the compact object is a Kerr black hole (BH), its quadrupole moment is expres…
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…
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 close limit approximation of binary black hole is a powerful method to study gravitational-wave emission from highly non-linear geometries. In this work, we use it as a tool to model black hole spacetimes in theories of gravity with a new fundamental scalar degree of freedom. As an example, we consider Einstein-scalar-Gauss-Bonnet gravity, which admits as solution the Schwarzschild geometry as well as black holes with scalar hair. Accordingly, we find scalar perturbations growing unbounded around binary systems. This "dynamical scalarization" process is easier to trigger (i.e. occurs at lo…
Black hole spectroscopy is the proposal to observe multiple quasinormal modes in the ringdown of a binary black hole merger. In addition to the fundamental quadrupolar mode, overtones and higher harmonics may be present and detectable in the gravitational wave signal, allowing for tests of the no-hair theorem. We analyze in detail the strengths and weaknesses of the standard Rayleigh criterion supplied with a Fisher matrix error estimation, and we find that the criterion is useful, but too restrictive. Therefore we motivate the use of a conservative high Bayes factor threshold to obtain the bl…
We investigate the prospect of using black hole spectroscopy to constrain the parameters of Horndeski gravity through observations of gravitational waves from perturbed black holes. We study the gravitational waves emitted during ringdown from black holes without hair in Horndeski gravity, demonstrating the qualitative differences between such emission in General Relativity and Horndeski theory. In particular, Quasi-Normal Mode frequencies associated with the scalar field spectrum can appear in the emitted gravitational radiation. Analytic expressions for error estimates for both the black hol…
The first two LIGO/Virgo observing runs have detected several black hole binary mergers. One of the most exciting prospects of future observing runs is the possibility to identify the remnants of these mergers as Kerr black holes by measuring their (complex) quasinormal mode frequencies. This idea - similar to the identification of atomic elements through their spectral lines - is sometimes called "black hole spectroscopy". Third-generation Earth-based detectors and the space-based interferometer LISA could measure multiple spectral lines from different multipolar components of the radiation, …
Scalar fields coupled to the Gauss-Bonnet invariant can undergo a tachyonic instability, leading to spontaneous scalarization of black holes. Studies of this effect have so far been restricted to single black hole spacetimes. We present the first results on dynamical scalarization in head-on collisions and quasicircular inspirals of black hole binaries with numerical relativity simulations. We show that black hole binaries can either form a scalarized remnant or dynamically descalarize by shedding off its initial scalar hair. The observational implications of these findings are discussed.
Results from regular monitoring of relativistic compact binaries like PSR 1913+16 are consistent with the dominant (quadrupole) order emission of gravitational waves (GWs). We show that observations associated with the binary black hole central engine of blazar OJ 287 demand the inclusion of gravitational radiation reaction effects beyond the quadrupolar order. It turns out that even the effects of certain hereditary contributions to GW emission are required to predict impact flare timings of OJ 287. We develop an approach that incorporates this effect into the binary black hole model for OJ~2…
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 …
