arXiv subjects

Kwinten Fransen

Publications and source records attributed to Kwinten Fransen.

18 recordsLinked to original sources

arXiv2026

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.

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arXiv2025

Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime

We compute a gravitational on-shell action of a finite, spherically symmetric causal diamond in $(d+2)$-dimensional Minkowski spacetime, finding it is proportional to the area of the bifurcate horizon $A_{\mathcal{B}}$. We then identify the on-shell action with the saddle point of the Euclidean gravitational path integral, which is naturally interpreted as a partition function. This partition function is thermal with respect to a modular Hamiltonian $K$. Consequently, we determine, from the on-shell action using standard thermodynamic identities, both the mean and variance of the modular Hamiltonian, finding $\langle K \rangle = \langle (ΔK)^2 \rangle = \frac{A_{\mathcal{B}}}{4 G_N}$. Finally, we show that modular fluctuations give rise to fluctuations in the geometry, and compute the associated phase shift of massless particles traversing the diamond under such fluctuations.

hep-th↗

arXiv2025

Perturbations of Plane Waves and Quadratic Quasinormal Modes on the Lightring

We study second order gravitational perturbations on plane wave spacetimes from both the metric and curvature perturbation points of view. For the former, we explicitly use the isometries of the background to introduce tensor oscillator harmonics, which render Einstein's equations algebraic around symmetric plane waves. For the latter, we formulate the first and second order Teukolsky equations in a Geroch-Held-Penrose covariant way. Both approaches are useful in their own right, and together with our discussion on gauge freedom, they provide a foundation for the study of higher-order gravitational dynamics around plane wave spacetimes. Taking the perspective that these plane wave spacetimes arise from Penrose limits, we subsequently use these results to explore the nonlinear gravitational dynamics close to black hole lightrings. Specifically, we define and discuss quadratic quasinormal mode ratios, observe that they satisfy emergent selection rules, and make publicly available a code to compute them.

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arXiv2025

Expanding on the double copy in null Fermi coordinates

We propose a Weyl classical double copy for a Fermi normal coordinate expansion around null geodesics. To leading order in this "Penrose expansion", we recover a previously proposed double copy of the Penrose limit. For spacetimes with an exact double copy, this Penrose limit double copy is extended to all orders. For spacetimes without such a double copy, generic obstructions appear at second subleading order. We thus argue that for any spacetime, near any null geodesic there is a classical double copy structure at least up to first subleading order in the Penrose expansion. Finally, we point out a difficulty in identifying an appropriate flat space to extend our results to the Kerr-Schild double copy, related to the generic incompatibility between Kerr-Schild and Penrose-Güven gauge.

hep-th↗

arXiv2024

The Penrose limit of the Weyl double copy

We embed the Penrose limit into the Weyl classical double copy. Thereby, we provide a lift of the double copy properties of plane wave spacetimes into black hole geometries and we open a novel avenue towards taking the classical double copy beyond statements about algebraically special backgrounds. In particular, the Penrose limit, viewed as the leading order Fermi coordinate expansion around a null geodesic, complements approaches leveraging asymptotic flatness such as the asymptotic Weyl double copy. Along the way, we show how our embedding of the Penrose limit within the Weyl double copy naturally fixes the functional ambiguity in the double copy for Petrov type N spacetimes. We also highlight the utility of a spinorial approach to the Penrose limit. In particular, we use this spinorial approach to derive a simple analytical expression for arbitrary Penrose limits of four-dimensional, vacuum type D spacetimes.

hep-th↗

arXiv2024

Gravitational wave signatures of departures from classical black hole scattering

We initiate a general investigation into gravitational wave signatures of modifications to scattering of gravitational radiation from black holes. Such modifications may be present due to the quantum dynamics that makes black holes consistent with quantum mechanics, or in other models for departures from classical black hole behavior. We propose a parameterization of the corrections to scattering as a physically meaningful, model-independent, and practical bridge between theoretical and observational aspects of the problem; this parameterization can incorporate different models in the literature. We then describe how these corrections influence the gravitational wave signal, e.g. of a body orbiting a much more massive black hole. In particular, they generically change the rate of energy emission; this effect can be leveraged over many orbits of inspiral to enhance the sensitivity to small corrections, as has been noticed in simple models. We provide preliminary estimates of the sensitivity of future gravitational wave observations to these corrections, and outline further work to be done to connect both to a more fundamental theory of quantum black holes, and to realistic observational situations.

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arXiv2023

Quasinormal modes of rotating black holes in higher-derivative gravity

We compute the spectrum of linearized gravitational excitations of black holes with substantial angular momentum in the presence of higher-derivative corrections to general relativity. We do so perturbatively to leading order in the higher-derivative couplings and up to order fourteen in the black hole angular momentum. This allows us to accurately predict quasinormal mode frequencies of black holes with spins up to about $70\%$ of the extremal value. For some higher-derivative corrections, we find that sizable rotation enhances the frequency shifts by almost an order of magnitude relative to the static case.

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arXiv2023

The universal Teukolsky equations and black hole perturbations in higher-derivative gravity

We reduce the study of perturbations of rotating black holes in higher-derivative extensions of general relativity to a system of decoupled radial equations that stem from a set of universal Teukolsky equations. We detail a complete computational strategy to obtain these decoupled equations in general higher-derivative theories. We apply this to six-derivative gravity to compute the shifts in the quasinormal mode frequencies with respect to those of Kerr black holes in general relativity. At linear order in the angular momentum we reproduce earlier results obtained with a metric perturbation approach. In contrast with this earlier work, however, the method given here applies also to post-merger black holes with significant spin, which are of particular observational interest.

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arXiv2023

Quasinormal Modes from Penrose Limits

We use Penrose limits to approximate quasinormal modes with large real frequencies. The Penrose limit associates a plane wave to a region of spacetime near a null geodesic. This plane wave can be argued to geometrically realize the geometrical optics approximation. Therefore, when applied to the bound null orbits around black holes, the Penrose limit can be used to study quasinormal modes. For instance, this Penrose limit point of view makes manifest the symmetry that emerges in the geometrical optics approximation of quasinormal modes in terms of isometries of the resulting plane wave spacetime. We apply the procedure to warped $\rm{AdS}_3$, Schwarzschild black holes and Kerr black holes. In the former we show explicitly how the symmetry algebra contracts to that of the limiting plane wave while in the latter we find the expected agreement with numerically computed quasinormal modes for large (real) frequencies.

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arXiv2022

New Horizons for Fundamental Physics with LISA

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas.

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arXiv2022

On Detecting Equatorial Symmetry Breaking with LISA

The equatorial symmetry of the Kerr black hole is generically broken in models of quantum gravity. Nevertheless, most phenomenological models start from the assumption of equatorial symmetry, and little attention has been given to the observability of this smoking gun signature of beyond-GR physics. Extreme mass-ratio inspirals (EMRIs), in particular, are known to sensitively probe supermassive black holes near their horizon; yet estimates for constraints on deviations from Kerr in space-based gravitational wave observations (e.g. with LISA) of such systems are currently based on equatorially symmetric models. We use modified "analytic kludge" waveforms to estimate how accurately LISA will be able to measure or constrain equatorial symmetry breaking, in the form of the lowest-lying odd parity multipole moments $S_2, M_3$. We find that the dimensionless multipole ratios such as $S_2/M^3$ will typically be detectable for LISA EMRIs with a measurement accuracy of $Δ(S_2/M^3) \sim 1\%$; this will set a strong constraint on the breaking of equatorial symmetry.

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arXiv2021

Gravitational ringing of rotating black holes in higher-derivative gravity

We study gravitational perturbations of slowly-rotating black holes in a general effective-field-theory extension of general relativity that includes up to eight-derivative terms. We show that two Schrödinger-like equations with spin-dependent effective potentials govern the odd - and even-parity master variables. These equations are coupled for parity-violating corrections, and this coupling affects the quasinormal modes even at linear order in the higher-derivative corrections, due to their isospectrality in general relativity. We provide results for the shifts in the fundamental quasinormal mode frequencies at linear order in the spin, which we expect to be valuable for high-precision phenomenology through future gravitational wave observations.

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arXiv2021

Modeling and detecting resonant tides of exotic compact objects

The event horizon of a black hole in general relativity absorbs all infalling radiation. Any observation of the contrary would immediately challenge the expectation that astrophysical black holes are described by the vacuum Kerr geometry. If a putative black hole does reflect part of the ingoing radiation, its quasinormal mode structure is drastically altered. Low frequency modes can be introduced that are resonantly excited during the inspiral of a binary system. We study the resulting phase shift of the gravitational wave signal. Building on neutron star results, we obtain a model-independent expression for the phase shift that depends only on quasinormal modes and Love numbers of the compact object. We find that the phase shift might be detectable with Einstein Telescope for asymmetric binaries in high signal-to-noise events ($\sim 10^3$), but by far cannot explore the Planck scale.

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arXiv2020

Novel higher-curvature variations of $R^2$ inflation

We put forward novel extensions of Starobinsky inflation, involving a class of 'geometric' higher-curvature corrections that yield second-order Friedmann-Lemaître equations and second-order-in-time linearized equations around cosmological backgrounds. We determine the range of models within this class that admit an extended phase of slow roll inflation as an attractor. By embedding these theories in anti-de Sitter space, we derive holographic 'unitarity' bounds on the two dominant higher-order curvature corrections. Finally we compute the leading corrections to the spectral properties of scalar and tensor primordial perturbations, including the modified consistency relation $r=-8n_{T}$. Remarkably, the range of models singled out by holography nearly coincides with the current observational bounds on the scalar spectral tilt. Our results indicate that future observations have the potential to discriminate between different higher-curvature corrections considered here.

hep-th↗

arXiv2020

Ringing of rotating black holes in higher-derivative gravity

We compute scalar quasinormal mode (QNM) frequencies in rotating black hole solutions of the most general class of higher-derivative gravity theories, to quartic order in the curvature, that reduce to General Relativity for weak fields and are compatible with its symmetries. The wave operator governing the QNMs is not separable, but we show one can extract the QNM frequencies by a projection onto the set of spheroidal harmonics. We have obtained accurate results for the quasinormal frequency corrections relative to Kerr for rotating black holes with dimensionless spins up to $\sim 0.7$. We also discuss to what extent our results carry over to the phenomenologically more relevant case of gravitational QNMs. Finally we provide an ancillary computational package that allows one to generalize our calculations to any effective energy-momentum tensor arising from higher-derivative terms in the effective action.

gr-qc↗

arXiv2020

Scalar Self-force for High Spin Black Holes

We semianalytically investigate the scalar self-force experienced in the final stages of extreme mass ratio inspirals of nonspinning scalar particles into supermassive nearly extremal Kerr black holes. We exploit the near-horizon conformal symmetry to find the self-force for general corotating equatorial geodesics. The angular component of the self-force is shown to be universal at leading order in the high spin limit. We verify that the energy and angular momentum losses of the scalar particle match with the asymptotic fluxes of scalar radiation. In particular, we relate the previously described persistent oscillations in the asymptotic energy and angular momentum fluxes with the local self-force. Such oscillations arise from traveling waves that prevent the near-horizon and the asymptotic region to fully decouple in the extremal limit. Conformal invariance is therefore reduced to discrete scale invariance with associated logarithmic periodicity.

gr-qc↗

arXiv2020

Transition from inspiral to plunge into a highly spinning black hole

We extend the Ori-Thorne-Kesden procedure to consistently describe the non-quasi-circular transition around the ISCO from inspiral to plunge into a black hole of arbitrary spin, including near-extremal. We identify that for moderate or high spins the transition is governed by the Painlevé transcendent equation of the first kind while for extremely high spins it is governed by a self-similar solution to the Korteweg-de Vries equation. We match the transition solution at leading order in the high spin limit with the analytical quasi-circular inspiral in the near-horizon region. We also show that the central black hole of an extreme mass ratio binary has a near-extremality parameter that scales at least as the mass ratio due to superradiant gravitational wave emission, which excludes extremely high spins.

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arXiv2019

Gravitational waves from plunges into Gargantua

We analytically compute time domain gravitational waveforms produced in the final stages of extreme mass ratio inspirals of non-spinning compact objects into supermassive nearly extremal Kerr black holes. Conformal symmetry relates all corotating equatorial orbits in the geodesic approximation to circular orbits through complex conformal transformations. We use this to obtain the time domain Teukolsky perturbations for generic equatorial corotating plunges in closed form. The resulting gravitational waveforms consist of an intermediate polynomial ringdown phase in which the decay rate depends on the impact parameters, followed by an exponential quasi-normal mode decay. The waveform amplitude exhibits critical behavior when the orbital angular momentum tends to a minimal value determined by the innermost stable circular orbit. We show that either near-critical or large angular momentum leads to a significant extension of the LISA observable volume of gravitational wave sources of this kind.

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