arXiv subjects

Adrien Kuntz

Publications and source records attributed to Adrien Kuntz.

At least 19 recordsLinked to original sources

arXiv2026

Vanishing of all redshift modes in Schwarzschild ringdown

Several studies of black hole ringdown from particles plunging into black holes have identified contributions decaying at integer multiples of the surface gravity, called redshift modes, horizon modes, and direct waves. We show that, for Schwarzschild black holes, every one of these contributions has vanishing amplitude in the observable waveform. The cancellation follows from causality, which forces the source-integrated Green function to vanish on the light cone. Individual quasi-normal mode overtones still carry non-zero redshift-mode contributions, but these cancel exactly once the sum over overtones is performed; the so-called impulsive contribution to the waveform acts precisely as the counterterm enforcing this cancellation. Finally, we provide a motivation to the standard regularization of quasinormal mode excitation coefficients since divergences give rise to vanishing redshift modes.

gr-qc↗

arXiv2026

When the Ringing Stops: Purely Imaginary Modes in the Ringdown Spectrum of Dynamical Black Holes

We extend the frequency-domain analysis of quasinormal modes in a dynamical, spherically symmetric black hole spacetime undergoing constant-rate mass evolution. In particular, we report a novel feature of the spectrum: the presence of purely imaginary eigenvalues in addition to the usual light-ring modes. We study the frequencies of these modes both analytically and numerically. The analytical calculation uses a novel formalism based on recent advances in connection coefficients of Heun functions. We then compute the frequencies numerically using a spectral method on hyperboloidal slices and find excellent agreement between the two approaches. Finally, we validate the frequency-domain results against an independent set of time-domain simulations. Our analysis shows that the purely imaginary modes govern the late-time signal through exponentially decaying tails. In the Schwarzschild limit, both frequency- and time-domain studies consistently show that the purely imaginary modes give rise to the familiar Schwarzschild power-law tail.

gr-qc↗

arXiv2026

Dynamical quasinormal mode excitation II: propagation and convergence in Schwarzschild

We study the dynamical excitation of quasinormal modes (QNMs) during the plunge of a particle into a Schwarzschild black hole, building on the framework of Phys. Rev. D 113 (2026) 2, 024048 (Paper I). Investigating the high-frequency behavior of Leaver's QNM solutions, we obtain a more accurate and general prescription for their propagation. We confirm the existence of a new "characteristic radius" for QNM excitation, the bounce radius $r_*=0$, in agreement with recent literature. To its right, the QNM signal scatters off this point before reaching the observer; to its left, it propagates directly on the light-cone. Applying the formalism of Paper I to inspiralling particles, and using this refined prescription, we obtain a QNM signal that accurately reproduces the oscillatory component of the waveform after the bounce crossing, yielding an essentially complete first-principles description of the waveform from shortly after the signal peak. The dynamical QNM signal undergoes a transition as the particle crosses the bounce radius: from a quasi-resonant regime, where successive overtones are driven in counter-phase and interfere destructively, to a free-oscillator one, where they are in phase and the QNM sum converges rapidly. These results provide a clear physical interpretation of the collective QNM behavior during the plunge, and a firm theoretical foundation for accurate ringdown modelling.

gr-qc↗

arXiv2026

Scalar emission from binary neutron stars in scalar-tensor theories with kinetic screening

We investigate the scalar emission from binary neutron stars in shift-symmetric scalar-tensor theories with kinetic screening ($K$-essence), using 3+1 numerical simulations in the decoupling limit. To construct static binary initial data in the regime where the screening radius $r_*$ greatly exceeds the orbital separation, we introduce a hyperbolization of the static field equations that bypasses the Keldysh-type breakdown affecting direct time evolutions. For equal-mass binaries, where the scalar emission is dominated by the $\ell=m=2$ mode, kinetic screening acts non-monotonically on the scalar radiation, suppressing or enhancing the quadrupolar amplitude depending on the relative size of $r_*$ and $\lambda_{22}$ (with $\lambda_{22}$ the wavelength): for $\lambda_{22}\ll r_*$ it is suppressed relative to the Fierz-Jordan-Brans-Dicke (FJBD) case, while for $\lambda_{22}\gtrsim r_*$ it is amplified above FJBD. For unequal-mass binaries a scalar dipole re-emerges, growing linearly with the mass asymmetry, while the quadrupolar screening remains close to the equal-mass case down to mass ratios $\sim 0.6$. The non-monotonic behavior of kinetic screening that we uncover has potential implications for gravitational-wave-based tests of gravity. The relativistic double pulsar, in particular, requires $r_*\gg 10^9$~km to efficiently suppress the scalar quadrupole; for cosmologically-motivated $\Lambda$, $r_*\sim 10^{11}$~km (for a solar-mass source), giving only moderate suppression.

gr-qc↗

arXiv2026

Looking for non-gaussianity in Pulsar Timing Arrays through the four point correlator

Pulsar Timing Arrays have recently reported strong evidence for a stochastic gravitational wave background. In standard analyses, it is modeled through pulsar-dependent Fourier coefficients assumed to follow gaussian statistics, so that the signal is fully characterized by its two-point function. However, if the background arises from a finite population of inspiralling supermassive black hole binaries, non-gaussian features may emerge, making the determination of higher-order correlators essential. In this work, we compute the complete four-point correlator of the stochastic gravitational wave background Fourier coefficients for four arbitrary pulsar positions, identifying it as the leading probe of non-gaussianity. The result separates into a gaussian contribution, proportional to the square of the two-point function, and a genuinely non-gaussian connected component, whose non-trivial angular dependence generalizes the Hellings and Downs correlation to four pulsars. This angular structure depends only on averages of products of antenna pattern functions, and is therefore expected to be independent of the specific physical origin of the background. We further propose to incorporate the four-point correlator into the parameter-estimation pipeline by deriving a marginalized likelihood that perturbatively accounts for non-gaussian effects. Our results provide the theoretical framework to search for non-gaussian features in pulsar timing array data, opening the way to a more complete characterization of gravitational-wave backgrounds.

gr-qc↗

arXiv2025

Green function of the P\"{o}schl-Teller potential

We use an approximation of the Regge-Wheeler-Zerilli potential, known as P\"{o}schl-Teller, to exactly compute the time-domain Green function of black hole perturbations in this simplified model, taking into account all causality conditions. We find the existence of an additional early times piece in the Green function, contributing to new exponentially growing modes just before the signal interacts with the maximum of the potential. The waveform itself is decomposed as an instantaneous piece traveling exactly on the light-cones of the Green function and a historical piece depending on the past trajectory of the system inside the light-cone. We also study redshift modes and show that the Regge-Wheeler-Zerilli Green function is regular at their frequency, with no zero nor pole.

gr-qc↗

arXiv2025

Searching for Gravitational Waves with Gaia and its Cross-Correlation with PTA: Absolute vs Relative Astrometry

Astrometric missions like Gaia provide exceptionally precise measurements of stellar positions and proper motions. Gravitational waves traveling between the observer and distant stars can induce small, correlated shifts in these apparent positions, a phenomenon known as astrometric deflection. The precision and scale of astrometric datasets make them well-suited for searching for a stochastic gravitational wave background, whose signature appears in the two-point correlation function of the deflection field across the sky. Although Gaia achieves high accuracy in measuring angular separations in its focal plane, systematic uncertainties in the satellite's absolute orientation limit the precision of absolute position measurements. These orientation errors can be mitigated by focusing on relative angles between star pairs, which effectively cancel out common-mode orientation noise. In this work, we compute the astrometric response and the overlap reduction functions for this relative astrometry approach, correcting previous expressions presented in the literature. We use a Fisher matrix analysis to compare the sensitivity of relative astrometry to that of conventional absolute astrometry. Our analysis shows that while the relative method is theoretically sound, its sensitivity is limited for closely spaced star pairs within a single Gaia field of view. Pairs with large angular separations could provide competitive sensitivity, but are practically inaccessible due to Gaia's scanning law. Finally, we demonstrate that combining astrometric data with observations from pulsar timing arrays leads to slight improvements in sensitivity at frequencies greater than approximately 10^-7 Hz.

gr-qc↗

arXiv2025

Systematic bias in LISA ringdown analysis due to waveform inaccuracy

Inaccurate modeling of gravitational-wave signals can introduce systematic biases in the inferred source parameters. As detector sensitivities improve and signals become louder, mitigating such waveform-induced systematics becomes increasingly important. In this work, we assess the systematic biases introduced by an incomplete description of the ringdown signal from massive black hole binaries in the LISA band. Specifically, we investigate the impact of mode truncation in the ringdown template. Using a reference waveform composed of 13 modes, we establish a mode hierarchy and determine the minimum number of modes required to avoid parameter biases across a wide range of LISA sources. For typical systems with masses $\sim 10^6$--$10^7\,M_\odot$ at redshifts $z \sim 2$--$6$, we find that at least 3--6 modes are needed for accurate parameter estimation, while high-SNR events may need at least 10 modes. Our results are a window-insensitive lower bound on the minimum number of modes, as more modes may be needed depending on the choice of time-domain windowing of the post-merger signal.

gr-qc↗

arXiv2025

Black hole spectroscopy: from theory to experiment

The "ringdown" radiation emitted by oscillating black holes has great scientific potential. By carefully predicting the frequencies and amplitudes of black hole quasinormal modes and comparing them with gravitational-wave data from compact binary mergers we can advance our understanding of the two-body problem in general relativity, verify the predictions of the theory in the regime of strong and dynamical gravitational fields, and search for physics beyond the Standard Model or new gravitational degrees of freedom. We summarize the state of the art in our understanding of black hole quasinormal modes in general relativity and modified gravity, their excitation, and the modeling of ringdown waveforms. We also review the status of LIGO-Virgo-KAGRA ringdown observations, data analysis techniques, and the bright prospects of the field in the era of LISA and next-generation ground-based gravitational-wave detectors.

gr-qc↗

arXiv2025

Probing supermassive black hole scalarization with Pulsar Timing Arrays

Scalar-tensor theories with a scalar field coupled to the Gauss-Bonnet invariant can evade no-hair theorems and allow for non-trivial scalar profiles around black holes. This coupling is characterized by a length scale $\lambda$, which, in an effective field theory perspective, sets the threshold below which deviations from General Relativity become significant. LIGO/VIRGO constraints indicate $\lambda$ is small, implying supermassive black holes should not scalarize. However, recent work suggests that scalarization can occur within a narrow window of masses, allowing supermassive black holes to scalarize, while leaving LIGO/VIRGO sources unaffected. We explore the impact of this scenario on the stochastic gravitational wave background recently observed by Pulsar Timing Arrays. We find that scalarization can alter the characteristic strain produced by circularly inspiralling SMBH binaries and that current data shows a marginal preference for a non-zero $\lambda$. However, similar signatures could arise from astrophysical effects such as orbital eccentricity or environmental interactions, emphasizing the need for improved modeling and longer observations to discriminate among the different scenarios.

gr-qc↗

arXiv2025

Ringdown nonlinearities in the eikonal regime

The eikonal limit of black hole quasinormal modes (the large multipole limit $\ell \gg 1$) can be realized geometrically as a next-to-leading order solution to the geometric optics approximation, and also as linear fluctuations about the Penrose limit plane wave adapted to the lightring. Extending this interpretation beyond the linear order in perturbation theory requires a robust understanding of quadratic quasinormal modes for large values of $\ell$. We analyze numerically the relative excitation of quadratic to linear quasinormal modes of Schwarzschild black holes, with two independent methods. Our results suggest that the ratio of quadratic to linear amplitudes for the $\ell \times \ell \to 2\ell$ channel converges towards a finite value for large $\ell$, in sharp contrast with a recent proposal inspired by the Penrose limit perspective. On the other hand, the $2 \times \ell \to \ell + 2$ channel seems to have a linearly growing ratio. Nevertheless, we show that there is no breakdown of black hole perturbation theory for physically realistic initial data.

gr-qc↗

arXiv2024

Scalar emission from neutron star-black hole binaries in scalar-tensor theories with kinetic screening

We explore scalar radiation from neutron star-black hole binaries in scalar-tensor theories with kinetic screening ($K$-essence). Using 3+1 numerical relativity simulations in the decoupling limit, we investigate scalar dipole and quadrupole radiation for different values of the strong coupling constant $\Lambda$. Our results show that kinetic screening effectively suppresses the scalar dipole radiation as $\Lambda$ decreases. This is validated by comparing to analytic predictions for the screening of dipole scalar emission, with which our numerical results show good agreement. However, our numerical simulations show that the suppression of scalar quadrupole radiation is less efficient, even when the screening radius exceeds the wavelength of the emitted radiation. In fact, the dependence of the scalar quadrupole amplitude on $\Lambda$ flattens out for the smallest $\Lambda$ that we can simulate, and the quadrupole amplitude is suppressed only by a factor $\lesssim 3$ relative to the Fierz-Jordan-Brans-Dicke case. Overall, our study shows that scalar quadrupole radiation from mixed binaries may be used to place constraints on $K$-essence theories with next-generation gravitational-wave detectors.

gr-qc↗

arXiv2024

Amplitudes and Polarizations of Quadratic Quasi-Normal Modes for a Schwarzschild Black Hole

General Relativity predicts the existence of quadratic quasi-normal modes at second order in perturbation theory. Building on our recent work, we compute the amplitudes and polarizations of these modes for non-rotating black holes, showing that they are completely determined by the amplitudes and polarizations of linear modes. We obtain the ratio of quadratic to linear amplitudes, which still depends on the initial conditions of the merger through the polarization of linear modes. However, we demonstrate that this dependence is captured by four fundamental numbers, independent of initial conditions, representing four different combinations of linear modes parities. Additionally, we prove two selection rules regarding the vanishing of classes of quadratic modes. Our results are available online as a package which provides the ratio of amplitudes across a broad spectrum of angular momenta.

hep-th↗

arXiv2024

Angular momentum sensitivities in scalar-tensor theories

Scalar-tensor theories have a long history as possible phenomenological alternatives to General Relativity, but are known to potentially produce deviations from the (strong) equivalence principle in systems involving self-gravitating objects, as a result of the presence of an additional gravitational scalar field besides the tensor modes of General Relativity. We describe here a novel mechanism whereby the equivalence principle is violated for an isolated rotating neutron star, if the gravitational scalar field is changing in time far from the system. We show that the neutron star rotational period changes due to an effective coupling ("angular momentum sensitivity") to the gravitational scalar, and compute that coupling for viable equations of state for nuclear matter. We comment on the relevance of our findings for testing scalar-tensor theories and models of ultralight dark matter with pulsar timing observations, a topic that we tackle in a companion paper.

gr-qc↗

arXiv2024

Quadratic Quasi-Normal Modes of a Schwarzschild Black Hole

Quadratic quasi-normal modes, generated at second order in black hole perturbation theory, are a promising target for testing gravity in the nonlinear regime with next-generation gravitational wave detectors. While their frequencies have long been known, their amplitudes remain poorly studied. We introduce regular variables and compute amplitudes for Schwarzschild black holes with the Leaver algorithm. We find a nonlinear ratio $\mathcal{R}\simeq0.154e^{-0.068i}$ for the most excited $\ell=4$ mode, matching results from Numerical Relativity. We also predict new low-frequency $\ell=2$ quadratic modes.

gr-qc↗

arXiv2024

Constraints on conformal ultralight dark matter couplings from the European Pulsar Timing Array

Millisecond pulsars are extremely precise celestial clocks: as they rotate, the beamed radio waves emitted along the axis of their magnetic field can be detected with radio telescopes, which allows for tracking subtle changes in the pulsars' rotation periods. A possible effect on the period of a pulsar is given by a potential coupling to dark matter, in cases where it is modeled with an "ultralight" scalar field. In this paper, we consider a universal conformal coupling of the dark matter scalar to gravity, which in turn mediates an effective coupling between pulsars and dark matter. If the dark matter scalar field is changing in time, as expected in the Milky Way, this effective coupling produces a periodic modulation of the pulsar rotational frequency. By studying the time series of observed radio pulses collected by the European Pulsar Timing Array experiment, we present constraints on the coupling of dark matter, improving on existing bounds. These bounds can also be regarded as constraints on the parameters of scalar-tensor theories of the Fierz-Jordan-Brans-Dicke and Damour-Esposito-Far\`{e}se types in the presence of a (light) mass potential term.

astro-ph.HE↗

arXiv2024

Nonlinear quasinormal mode detectability with next-generation gravitational wave detectors

In the aftermath of a binary black hole merger event, the gravitational wave signal emitted by the remnant black hole is modeled as a superposition of damped sinusoids known as quasinormal modes. While the dominant quasinormal modes originating from linear black hole perturbation theory have been studied extensively in this post-merger "ringdown" phase, more accurate models of ringdown radiation include the nonlinear modes arising from higher-order perturbations of the remnant black hole spacetime. We explore the detectability of quadratic quasinormal modes with both ground- and space-based next-generation detectors. We quantify how predictions of the quadratic mode detectability depend on the quasinormal mode starting times. We then calculate the signal-to-noise ratio of quadratic modes for several detectors and binary black hole populations, focusing on the ($220\times220$) mode - i.e., on the quadratic term sourced by the square of the linear $(220)$ mode. For the events with the loudest quadratic mode signal-to-noise ratios, we additionally compute statistical errors on the mode parameters in order to further ascertain the distinguishability of the quadratic mode from the linear quasinormal modes. The astrophysical models used in this paper suggest that while the quadratic mode may be detectable in at most a few events with ground-based detectors, the prospects for detection with the Laser Interferometer Space Antenna (LISA) are more optimistic.

gr-qc↗

arXiv2023

Nonlinear Quasi-Normal Modes: Uniform Approximation

Recent works have suggested that nonlinear (quadratic) effects in black hole perturbation theory may be important for describing a black hole ringdown. We show that the technique of uniform approximations can be used to accurately compute 1) nonlinear amplitudes at large distances in terms of the linear ones, 2) linear (and nonlinear) quasi-normal mode frequencies, 3) the wavefunction for both linear and nonlinear modes. Our method can be seen as a generalization of the WKB approximation, with the advantages of not losing accuracy at large overtone number and not requiring matching conditions. To illustrate the effectiveness of this method we consider a simplified source for the second-order Zerilli equation, which we use to numerically compute the amplitude of nonlinear modes for a range of values of the angular momentum number.

hep-th↗