Ringdown Phase Research Articles

Searching for ultralight bosons with supermassive black hole ringdown

One class of competitive candidates for dark matter is ultralight bosons. If they exist, these bosons may form long-lived bosonic clouds surrounding rotating black holes via superradiant instabilities, acting as sources of gravity and affecting the propagation of gravitational waves around the host black hole. During extreme-mass-ratio inspirals, the bosonic clouds will survive the inspiral phase and can affect the quasinormal-mode frequencies of the perturbed black-hole--bosonic-cloud system. In this work, we compute the shifts of gravitational quasinormal-mode frequencies of a rotating black hole due to the presence of a surrounding bosonic cloud. We then perform a mock analysis on simulated Laser Interferometer Space Antenna observational data containing injected ringdown signals from supermassive black holes with and without a bosonic cloud. We find that with less than an hour of observational data of the ringdown phase of nearby supermassive black holes such as Sagittarius A* and M32, we can rule out or confirm the existence of cloud-forming ultralight bosons of mass $\ensuremath{\sim}{10}^{\ensuremath{-}17}\text{ }\text{ }\mathrm{eV}$.

Merger-ringdown consistency: A new test of strong gravity using deep learning

The gravitational waves emitted during the coalescence of binary black holes are an excellent probe to test the behaviour of strong gravity. In this paper, we propose a new test called the `merger-ringdown consistency test` that focuses on probing the imprints of the dynamics in strong-gravity around the black-holes during the plunge-merger and ringdown phase. Furthermore, we present a scheme that allows us to efficiently combine information across multiple ringdown observations to perform a statistical null test of GR using the detected BH population. We present a proof-of-concept study for this test using simulated binary black hole ringdowns embedded in the next-generation ground-based detector noise. We demonstrate the feasibility of our test using a deep learning framework, setting a precedence for performing precision tests of gravity with neural networks.

Importance of mirror modes in binary black hole ringdown waveform

The post-merger signal in binary black hole merger is described by linear, black-hole perturbation theory. Historically, this has been modeled using the dominant positive-frequency (corotating) fundamental mode. Recently, there has been a renewed effort in modeling the post-merger waveform using higher, positive-frequency overtones in an attempt to achieve greater accuracy in describing the waveform at earlier times using linear perturbation theory. It has been shown that the inclusion of higher overtones can shift the linear regime to the peak of $(l,m)=(2,2)$ spherical harmonic mode. In this work, we show that the inclusion of negative-frequency (counterrotating) modes, called 'mirror' modes, extends the validity of linear perturbation theory to even earlier times, with far lower systematic uncertainties in the model in recovering the remnant parameters at these early times. A good description of the signal at early times also enables for a greater signal-to-noise ratio to be accumulated in the ringdown phase, thereby, allowing for a more accurate measurement of remnant parameters and tests of general relativity.

Ergoregion instability and echoes for braneworld black holes: Scalar, electromagnetic, and gravitational perturbations

In the context of higher dimensional braneworld scenario, we have argued that the occurrence of horizonless exotic compact objects, as an alternative to classical black holes, are more natural. These exotic compact objects carry a distinctive signature of the higher dimension, namely a tidal charge parameter, inherited from the projection of the higher dimensional Weyl tensor onto the four dimensional spacetime we live in. Due to the absence of any horizon, rotating exotic compact objects are often unstable because of superradiance. Interestingly, these higher dimensional exotic compact objects, in the presence of the tidal charge, are more stable than their four dimensional counterpart. A similar inference is drawn by analysing the static modes associated with these exotic compact objects, irrespective of the nature of the perturbation i.e., it holds true for scalar, electromagnetic and also gravitational perturbation. The post-merger ringdown phase of the exotic compact object in the braneworld scenario, which can be described in terms of the quasi-normal modes, holds plethora of information regarding the nature of the higher dimension. In this connection we have discussed the analytical computation of the quasi-normal modes as well as their numerical estimation for perturbations of arbitrary spin, depicting existence of echoes in the ringdown waveform. As we have demonstrated, the echoes in the ringdown waveform depends explicitly on the tidal charge parameter and hence its future detection can provide constraints on the tidal charge parameter, which in turn will enable us to provide a possible bound on the length of the extra dimension.

Chaotic solutions and black hole shadow in f(R) gravity

We discuss the emergence of black hole shadow and photon-sphere in the context of f(R) gravity. It is shown that the shadow is exponentially sensitive to linear instabilities of metric coming from some f(R) solutions. Thus, the instabilities of photon circular trajectories, delimiting the black hole photon-sphere, are double exponentialized. Specifically we individuate two Lyapunov exponents, rather than only one, related to two different sources of chaos in geodesic orbits as a sort of butterfly effect. Such a result violates the black hole chaos bound proposed by Maldacena, Shenker and Stanford for General Relativity. We also explore the impact of the black hole metric instabilities in f(R) gravity on the quasi-normal modes. In the framework of Extended Theories of Gravity, our analysis suggests a new paradigm to deal with black hole shadow and gravitational waves observations coming from black hole merging in the ringdown phase.

Quantum black hole spectroscopy: probing the quantum nature of the black hole area using LIGO–Virgo ringdown detections

We present a thorough observational investigation of the heuristic quantised ringdown model presented by Foit and Kleban (2019 Class. Quantum Grav. 36 035006). This model is based on the Bekenstein–Mukhanov conjecture, stating that the area of a black hole (BH) horizon is an integer multiple of the Planck area multiplied by a phenomenological constant, α, which can be viewed as an additional BH intrinsic parameter. Our approach is based on a time-domain analysis of the gravitational wave (GW) signals produced by the ringdown phase of binary BH mergers detected by the LIGO and Virgo collaboration. Employing a full Bayesian formalism and taking into account the complete correlation structure among the BH parameters, we show that the value of α cannot be constrained using only GW150914, in contrast to what was suggested by Foit and Kleban (2019 Class. Quantum Grav. 36 035006). We proceed to repeat the same analysis on the new GW events detected by the LIGO and Virgo Collaboration up to 1 October 2019, obtaining a combined-event measure equal to and a combined log odds ratio of 0.1 ± 0.6, implying that current data are not informative enough to favor or discard this model against general relativity. We then show that using a population of GW150914-like simulated events—detected by the current infrastructure of ground-based detectors at their design sensitivity—it is possible to confidently falsify the quantised model or prove its validity, in which case probing α at the few % level. Finally we classify the stealth biases that may show up in a population study.

String memories ... lost and regained

We discuss stringy α′ corrections to the gravitational wave signal generated in the merging of two black holes. We model the merging with two BPS compact massive objects in the heterotic string, described by standard vertex operators or coherent states. Despite the expected cubic suppression in α′ w.r.t. the General Relativity result in the low-energy expansion, at tree level the infinite tower of string resonances leaves a clear footprint on the gravitational wave signals within the sensitivity region of aLIGO/VIRGO and future interferometers. Including loop effects that broaden and destabilise the string resonances suggests a sort of lost stringy memory effect that can be regained through the analysis of the quasi normal modes in the ring-down phase.

Gravitational wave echoes from black holes in massive gravity

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 finding provides a clear-cut way to test massive gravity theory using gravitational wave observations.

Scattering of axial gravitational wave pulses by monopole black holes and QNMs: a semianalytic approach

We study scattering of short Gaussian pulses of axial gravitational waves by a spherically symmetric black hole that has swallowed one or more global monopoles. We qualitatively show how the response of the black hole to the impinging pulses depends both on the number of monopoles the black hole has swallowed and on the symmetry breaking scale of the model which gave rise to the monopoles. We use semianalytical methods to determine the corresponding quasinormal modes that get excited by the impinging pulses and that get imprinted in the black hole’s response to the pulses. When generalized to the case of rotating black holes, such modes are also expected to show up in various other dynamical processes such as the ringdown phase of a binary black hole merger in case at least one of the companion black holes of the binary has swallowed one or more global monopoles.

Computation of displacement and spin gravitational memory in numerical relativity

We present the first numerical relativity waveforms for binary black hole mergers produced using spectral methods that show both the displacement and the spin memory effects. Explicitly, we use the SXS Collaboration's $\texttt{SpEC}$ code to run a Cauchy evolution of a binary black hole merger and then extract the gravitational wave strain using $\texttt{SpECTRE}$'s version of a Cauchy-characteristic extraction. We find that we can accurately resolve the strain's traditional $m=0$ memory modes and some of the $m\not=0$ oscillatory memory modes that have previously only been theorized. We also perform a separate calculation of the memory using equations for the Bondi-Metzner-Sachs charges as well as the energy and angular momentum fluxes at asymptotic infinity. Our new calculation uses only the gravitational wave strain and two of the Weyl scalars at infinity. Also, this computation shows that the memory modes can be understood as a combination of a memory signal throughout the binary's inspiral and merger phases, and a quasinormal mode signal near the ringdown phase. Additionally, we find that the magnetic memory, up to numerical error, is indeed zero as previously conjectured. Lastly, we find that signal-to-noise ratios of memory for LIGO, the Einstein Telescope (ET), and the Laser Interferometer Space Antenna (LISA) with these new waveforms and new memory calculation are larger than previous expectations based on post-Newtonian or Minimal Waveform models.

Ultra-long-lived quasi-normal modes of neutron stars in massive scalar-tensor gravity

The spectrum of frequencies and characteristic times that compose the ringdown phase of gravitational waves emitted by neutron stars carries information about the matter content (the equation of state) and the underlying theory of gravity. Typically, modified theories of gravity introduce additional degrees of freedom/fields, such as scalars, which result in new families of modes composing the ringdown spectrum. Simple but physically promising candidates are scalar-tensor theories, which effectively introduce an additional massive scalar field (i.e., an ultra-light boson) that couples non-minimally to gravity, resulting in scalarized neutron stars. Here we present the first calculation of the full ringdown spectrum in such theories. We show that the ringdown spectrum of neutron stars with ultra-light bosons is much richer and fundamentally different from the spectrum in general relativity and that it possesses propagating ultra-long-lived modes.

Echoes from braneworld black holes

The holographic interpretation of the Randall-Sundrum model based on the adaptation of the AdS/CFT correspondence to the braneworld scenario states that the black holes localized on the brane are {\it quantum corrected}. This can be better understood from the fact that the classical $AdS_{5}$ bulk dynamics is dual to gravity coupled with CFT on the four dimensional brane. Based on the back reaction of the CFT on the classical black hole geometry, localized on the brane, it is expected that there exist possible near horizon modifications. This may result in the black hole horizon becoming partially reflective, thus giving rise to echoes in the ringdown signal in gravitational wave observations. In this paper, we investigate the existence of such echoes in the ringdown phase of a black hole localized on the brane, carrying a \emph{negative} tidal charge, and establish the layout for future investigation of higher dimensional effects in the ringdown signal. Confirmed detections of echoes at the current levels of instrumental sensitivity can constrain the dimensionless value of tidal charge to $|Q| \lesssim M^2$ .

Spicing up the recipe for echoes from exotic compact objects: Orbital differences and corrections in rotating backgrounds

Recently, it has been argued that near-horizon modifications of the standard (classical) black hole spacetime could lead to observable alterations of the gravitational waveform generated by a binary black hole coalescence. Such modifications can be inspired by quantum gravity considerations, resulting in speculative horizonless exotic compact objects (ECOs) with no singularities, which may be an alternative to the classical black hole solution. A largely model-independent description of these objects proposed in the literature relies on the introduction of a partially reflective wall at some small distance away from the ``would-be'' horizon. The inspiral-merger ringdown of a pair of such objects would be subject to possibly detectable deviations from the black hole case due to matter effects. In particular, the ringdown phase would be modified by the late emergence of so-called ``echoes'' in the waveform, but most studies so far have considered spherically symmetric backgrounds. We use an in-falling scalar charge as an initial perturbation to simulate the excitation of the echoes of a rotating ECO, and we explore both the corotating and counterrotating cases, which provide distinct signals. In particular, rotation breaks the symmetry between positive and negative frequencies and introduces a subdominant frequency contribution in each echo, which we examine here for the first time. Our results follow consistently from the solution of the Teukolsky equation using the MST method developed by Mano, Suzuki, and Takasugi and the construction of the complex Green's function integrated over different particle geodesics.

Quasinormal modes, echoes and the causal structure of the Green's function

Quasinormal modes describe the return to equilibrium of a perturbed system, in particular the ringdown phase of a black hole merger. But as globally-defined quantities, the quasinormal spectrum can be highly sensitive to global structure, including distant small perturbations to the potential. In what sense are quasinormal modes a property of the resulting black hole? We explore this question for the linearized perturbation equation with two potentials having disjoint bounded support. We give a composition law for the Wronskian that determines the quasinormal frequencies of the combined system. We show that over short time scales the evolution is governed by the quasinormal frequencies of the individual potentials, while the sensitivity to global structure can be understood in terms of echoes. We introduce an echo expansion of the Green's function and show that, as expected on general grounds, at any finite time causality limits the number of echoes that can contribute. We illustrate our results with the soluble example of a pair of δ-function potentials. We explicate the causal structure of the Green's function, demonstrating under what conditions two very different quasinormal spectra give rise to very similar ringdown waveforms.

A WKB formula for echoes

We present a unified approach for the study of idealized gravitational compact objects like wormholes (WHs) and horizonless stars, here simulated by the presence of boundary conditions at a deeply inner wall. At the classical level, namely neglecting quantum effects, the presence of the wall leads to characteristic echoes following the usual ringdown phase, such that it can discriminate black holes from other horizonless, and probably exotic, compact objects. With regard to this issue, an analytical though approximated expression for the complex frequencies of the quasinormal echoes is found and discussed. At the quantum level, we show that static WHs do not radiate.

Analogue black hole spectroscopy; or, how to listen to dumb holes

Spectroscopy is a fundamental tool in science which consists in studying the response of a system as a function of frequency. Among its many applications in Physics, Biology, Chemistry and other fields, the possibility of identifying objects and structures through their emission spectra is remarkable and incredibly useful. In this paper we apply the spectroscopy idea to a numerically simulated hydrodynamical flow, with the goal of developing a new, non-invasive flow measurement technique. Our focus lies on an irrotational draining vortex, which can be seen, under specific conditions, as the analogue of a rotating black hole (historically named a dumb hole). This paper is a development of a recent experiment that suggests that irrotational vortices and rotating black holes share a common relaxation process, known as the ringdown phase. We apply techniques borrowed from black hole physics to identify vortex flows from their characteristic spectrum emitted during this ringdown phase. We believe that this technique is a new facet of the fluid-gravity analogy and constitutes a promising way to investigate experimentally vortex flows in fluids and superfluids alike.

On gravitational echoes from ultracompact exotic stars

At the dawn of a golden age for gravitational wave astronomy, we must leave no stone unturned in our quest for new phenomena beyond our current understanding of General Relativity (GR), particle physics and nuclear physics. In this paper we discuss gravitational echoes from ultracompact stars. We restrict our analysis to exact solutions of Einstein field equations in GR that are supported by an isotropic fluid with a physically motivated equations of state (EoS), and in particular we impose the constraint of causality. Our main conclusion is that ultracompact objects belonging to this category are not able to generate gravitational echoes like those that characterize the relaxation phase of a putative black hole mimicker. Nevertheless, we identify a class of physical exotic objects that are compact enough to accommodate the presence of an external unstable light ring, thus opening the possibility of trapping gravitational radiation and affecting the ringdown phase of a merger event. Most importantly, we show that once rotation is included these stars—contrary to what usually expected for ultracompact objects—are not plagued by any ergoregion instability. We extend our analysis for arbitrary values of angular velocity up to the Keplerian limit, and we comment about potential signals relevant for gravitational wave interferometers.

Probing microstructure of black hole spacetimes with gravitational wave echoes

Quantum nature of black hole horizons has been a subject of recent interest and scrutiny. In particular, a near-horizon quantum violation of the equivalence principle has been proposed as a resolution of the black hole information paradox. Such a violation may lead to a modified dispersion relation at high energies, which could become relevant due to the intense gravitational blueshift experienced by ingoing gravitational waves. We investigate the ringdown for a perturbed black hole with such a modified dispersion relation and find that infalling gravitational waves are partially reflected near the horizon. This results in the appearance of late-time ${\it echoes}$ in the ringdown phase of black hole merger events, with similar properties to those (arguably) seen in the Advanced LIGO observations. Current measurements suggest a Lorentz-violation scale of $10^{13 \pm 2}$ GeV for gravitational waves, with comparable dissipation and dispersion. Therefore, if confirmed, black hole ringdown echoes probe the microstructure of horizons and thus can test Lorentz-violating UV completions, such as in Ho$\v{r}$ava-Lifshitz gravity.

Effective field theory of black hole quasinormal modes in scalar-tensor theories

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 from Schwarzschild is small, we use the WKB method to introduce the notion of “light ring expansion”. This approximation is analogous to the slow-roll expansion used for inflation, and it allows us to express the quasinormal mode spectrum in terms of a small number of parameters. This work is a first step in describing, in a model independent way, how the scalar hair can affect the ringdown stage and leave signatures on the emitted gravitational wave signal. Potential signatures include the shifting of the quasi-normal spectrum, the breaking of isospectrality between polar and axial modes, and the existence of scalar radiation.

Quasinormal Modes of Modified Gravity (MOG) Black Holes

Black holes play a fundamental role in modern physics. These possess characteristic resonant frequencies, called Quasinormal Modes (QNMs), which are important in our understanding of the dynamics of astrophysical black holes. Quasinormal modes are single frequency modes dominating the time evolution of perturbations of systems which are subject to damping, either by internal dissipation or by radiating away energy. Due to the damping, the frequency of a quasinormal mode must be complex, its imaginary part being inversely proportional to the typical damping time. In general relativity, damping occurs even without friction, since energy may be radiated away towards infinity by gravitational waves. In this thesis, the quasinormal modes for gravitational and electromagnetic perturbations are calculated in a Scalar-Tensor-Vector (STVG) Modified Gravity (MOG) spacetime. This theory is based on an action principle and postulates the existence of a vector field, while elevating the three constants of the theory to scalar fields. In the weak-field approximation, STVG produces a Yukawa-like modification of the gravitational force due to a point source. STVG has been used successfully to explain galaxy rotation curves, the mass profiles of galaxy clusters, gravitational lensing in the Bullet Cluster, and cosmological observations without the need for dark matter. It is found that for the increasing model parameter α, both the real and imaginary parts of the QNMs decrease compared to those for a Schwarzschild black hole. On the other hand, when taking into account the 1/(1 + α) mass re-scaling factor present in MOG, Im(ω) matches almost identically that of GR, while Re(ω) is higher. These results can be identified in the ringdown phase of massive compact object mergers, and are thus timely in light of the recent gravitational wave detections by LIGO.