arXiv subjects

Carlos F. Sopuerta

Publications and source records attributed to Carlos F. Sopuerta.

At least 19 recordsLinked to original sources

arXiv2026

Probing Kerr symmetry breaking with LISA extreme-mass-ratio inspirals

[abridged] Extreme-mass-ratio inspirals (EMRIs) are one of the main sources of gravitational waves (GWs) for LISA. The large number of GW cycles in the EMRI signal makes them very precise probes of the local spacetime geometry that are highly sensitive to deviations from the Kerr metric. Here, we investigate EMRIs around generic, non-Kerr compact objects characterized by a rich multipolar structure. At leading post-Newtonian and linear mass-ratio orders, we incorporate in the waveform model both the axisymmetric and nonaxisymmetric components of the mass quadrupole and octupole moments, parametrizing in this way the breaking of two fundamental symmetries of the Kerr metric. We study the impact of these modifications on the waveform in the philosophy of the EMRI \emph{analytic kludge} models. In our case, the orbital evolution follows from a Lagrangian that contains of the multipolar structure of the primary, including for the first time the nonaxisymmetric multipole moments that break axial symmetry. Then, we assess the capability of LISA to constrain deviations of the multipole moments from their Kerr values and detecting symmetry-breaking effects. In this way, we analyze how effectively LISA will be able to probe models that predict horizon-scale modifications, such as the fuzzball model. Our results show that future LISA observations of EMRIs will provide unprecedented tests of the black hole structure and the underlying theory of gravity. In particular, with one year of LISA data from the inspiral of a $10\,M_{\odot}$ compact object into a rotating supermassive black hole of $10^{6}\,M_{\odot}$ and signal-to-noise ratio of 30, it will be possible to place tight bounds on deviations from the two fundamental symmetries of the Kerr metric, constraining equatorial symmetry breaking in the mass multipole sector to the $10^{-1}$ level and axial symmetry breaking to the $10^{-2}$ level.

gr-qc↗

arXiv2026

Probing fuzzballs and beyond: Model-independent tests of Kerr symmetry breaking with LISA

Gravitational waves provide a unique probe of the strong-field regime of gravity, offering access to physics beyond the classical black hole paradigm. We explore how space-based observations of extreme-mass-ratio inspirals (EMRIs) by the Laser Interferometer Space Antenna (LISA) can be used to test for departures from the Kerr geometry, and in particular for the breaking of its axial and equatorial symmetries, as expected in quantum-gravity-inspired alternatives to Kerr black holes such as the fuzzball proposal. By introducing generic multipolar deformations encoding potential symmetry breakings and performing a systematic parameter estimation analysis, we forecast LISA's ability to constrain such departures from the Kerr geometry in the strong-field regime. We show that EMRI signals with realistic signal-to-noise ratios can constrain several higher-order multipoles of the primary, opening a new observational window onto strong-field deviations from the Kerr geometry. In particular, we find that LISA can constrain generic nonaxisymmetric mass quadrupole deformations at the $10^{-4}-10^{-2}$ level and axisymmetric mass octupole deformations at the $10^{-1}$-$10^{0}$ level, providing concrete observational targets for strong-field deviations from the Kerr geometry, such as those that may arise in fuzzball and other exotic-compact-object scenarios. Our results demonstrate that precision measurements of EMRI waveforms will transform LISA into a powerful laboratory for fundamental physics and offer precise constraints on quantum-gravity-motivated models of compact objects.

hep-th↗

arXiv2026

GUEST: Gravitational Universe Exploration with Satellite Tracking. A passive satellite laser-ranging mission for the dark gravitational Universe

GUEST is a space mission concept whose central objective is the detection of gravitational waves (GWs) in the microhertz band -- a physics-rich frequency window that no other present or planned detector can reach at a significant level. The concept is simple: two dense, passive spheres, covered with cube-corner retroreflectors, deployed in {highly eccentric} Earth orbits ($e \gtrsim 0.7$, period $P \gtrsim 33$ h), tracked continuously by the global network of satellite laser-ranging stations over a minimum observation time of 10 years, with an expected total duration of 30 years. The orbits themselves act as resonant detectors of the oscillating gravitational perturbations, with the microhertz sensitivity emerging from the selected orbital parameters. From the same data stream, GUEST delivers a programme of fundamental and applied science that cuts across particle physics, gravitational-wave astronomy, cosmology, astrophysics, and geodesy: the first coherent search for GWs from supermassive black-hole binaries in the $μ$Hz band, the exploration of primordial GW backgrounds in the unexplored energy-scale gap between pulsar-timing arrays and LISA, a dedicated probe of ultra-light dark matter in a parameter region untouched by any other experiment, a new way to search for ultra-light bosons, order-of-magnitude-improved tests of new gravitational interactions at astronomical ranges, and a step change in the absolute determination of $GM_\oplus$ that underpins the Global Geodetic Observing System and future navigation and Earth-observation missions. This white paper presents the motivation, scientific reach, and mission concept of GUEST.

astro-ph.CO↗

arXiv2026

Hamiltonian formalism, master functions and Darboux transformations for perturbed (interiors and exteriors of) nonrotating black holes

Motivated by their relevance to the interior of nonrotating black holes, classical and quantum Kantowski-Sachs cosmologies have recently attracted increasing attention. This interest has led to the development of a Hamiltonian formalism for axial and polar perturbations, which can be extended to applications in the exterior region. The formalism provides also a description of the background physical degrees of freedom. Moreover, it allows for the construction of all physical perturbative gauge invariants, which can be arranged into canonical pairs associated with master functions. In this work, we review the basis of this Hamiltonian formalism, putting the emphasis on its foundations and fundamental steps rather than on details of the involved calculations. Our discussion focuses on classical and effective aspects, although we also briefly comment on its natural role in the quantization of perturbed black holes. Adopting this formalism we present a geometric interpretation of Darboux transformations between pairs of master functions, characterizing them as generalized canonical transformations that preserve the Hamiltonian structure of the perturbations as harmonic oscillators subject to certain potentials. This bijective correspondence between such canonical transformations and Darboux transformations, which was recently proved to hold for axial perturbations, is here extended to the case of polar perturbations. In addition, we demonstrate the existence of canonical transformations that, similarly to Darboux transformations, mix axial and polar master functions.

gr-qc↗

arXiv2026

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

gr-qc↗

arXiv2026

Master variables and Darboux symmetry for axial perturbations of the exterior and interior of black hole spacetimes

Recent efforts have shown that Kantowski-Sachs spacetime provides a useful framework for analyzing perturbations inside a Schwarzschild black hole (BH). In these studies, the adoption of a Hamiltonian formulation offers an insightful perspective. The aim of this work is twofold. First, we revisit and elaborate the results obtained so far in Kantowski-Sachs, with the focus placed on axial perturbations. In particular, by exploiting the relation between this spacetime and the interior of a nonrotating BH, we consider the extension of those results to the exterior geometry of the BH. In this way, we clarify the relation between the axial perturbative gauge invariants emerging from the canonical analysis and the already well-established axial BH invariants, often referred to as master functions. We do so by providing a unified picture of the Hamiltonian formalism, which does not distinguish, formally, between exterior and interior geometries. The second objective is to explore the role of Darboux transformations, which were found as hidden symmetries in the context of BH perturbations, and their appearance in the Hamiltonian setting. Within this framework, the Hamiltonian formulation provides a clear geometric interpretation and characterization of Darboux transformations within the axial sector, viewing them as the set of canonical transformations between Hamiltonians for axial master functions.

gr-qc↗

arXiv2025

Asymptotics and Universality in Black Holes: from the quasinormal Weyl's law to the binary merger waveform

Current state-of-the-art approaches to black hole (BH) dynamics, encompassing several effective approximation schemes, offer a remarkable control of the quantitative aspects of strong gravity. They also provide key insights into some qualitative aspects of the problem. In spite of this, there remain blind spots that hinder the understanding of the mechanisms underlying some observed phenomena, in particular concerning simplicity and universality in BH spacetimes. Adopting an 'asymptotic reasoning' approach, by filtering non-essential degrees of freedom, can potentially unveil universality patterns by identifying key underlying structural stability mechanisms. We first illustrate such an asymptotic approach by focusing on a BH quasinormal (QNM) Weyl's law, that accounts for the universal asymptotics of the QNM "counting function". This permits to identify light-trapping and the (local) redshift effect as the underlying mechanisms, also offering a bridge to the universal patterns found in BH QNM spectral instability. As a by-product, Weyl's law universality formally opens an observational access to spacetime (effective) dimensionality. More heuristically, we sketch a program recently put forward to apply such 'asymptotic reasoning' to address the observed simplicity and universality patterns in binary BH merger dynamics. This program is built as a hierarchy of asymptotic models, potentially making contact with integrability theory in gravity, namely through the background sector in a "wave-mean flow" approach to BH binary dynamics.

gr-qc↗

arXiv2025

Korteweg-de Vries Integrals for Modified Black Hole Potentials: Instabilities and other Questions

Quasi-normal modes (QNMs) and greybody factors are some of the most characteristic features of the dynamics of black holes (BHs) and represent the basis for a number of fundamental physics tests with gravitational wave observations. It is therefore important to understand the properties of these quantities, naturally introduced within BH perturbation theory, in particular the stability properties under modifications of the BH potential. Instabilities in the QNMs have been recently shown to appear in the BH pseudospectrum under certain circumstances. In this work, we give a novel point of view based on the existence of some recently discovered hidden symmetries in BH dynamics and the associated infinite series of conserved quantities, the Korteweg-de Vries (KdV) integrals. We provide different motivations to use the KdV integrals as indicators of some crucial BH spectral properties. In particular, by studying them in different scenarios described by modified BH barriers, we find strong evidence that the KdV conserved quantities represent a useful tool to look for instabilities in the BH spectrum of QNMs and in their greybody factors.

gr-qc↗

arXiv2025

Modified Black Hole Potentials and Their Korteweg-de Vries Integrals: Instabilities and Beyond

Black Hole (BH) Quasi-Normal Modes (QNMs) and Greybody Factors (GBFs) are key signatures of BH dynamics that are crucial for testing fundamental physics via gravitational waves. Recent studies of the BH pseudospectrum have revealed instabilities in QNMs. Here, we introduce a new perspective using hidden symmetries in the BH dynamics, specifically the Korteweg-de Vries (KdV) integrals - an infinite series of conserved quantities. By analyzing modified BH potentials, we find strong evidence that KdV integrals are valuable indicators for detecting instabilities in QNMs and GBFs.

gr-qc↗

arXiv2025

Simulation-based Inference of Massive Black Hole Binaries using Sequential Neural Likelihood

We propose a machine learning-based approach for parameter estimation of Massive Black Hole Binaries (MBHBs), leveraging normalizing flows to approximate the likelihood function. By training these flows on simulated data, we can generate posterior samples via Markov Chain Monte Carlo with a relatively reduced computational cost. Our method enables iterative refinement of smaller models targeting specific MBHB events, with significantly fewer waveform template evaluations. However, dimensionality reduction is crucial to make the method computationally feasible: it dictates both the quality and time efficiency of the method. We present initial results for a single MBHB with Gaussian noise and aim to extend our work to increasingly realistic scenarios, including waveforms with higher modes, non-stationary noise, glitches, and data gaps.

gr-qc↗

arXiv2025

STE-QUEST -- Space Time Explorer and QUantum Equivalence principle Space Test: The 2022 medium-class mission concept

Space-borne quantum technologies, particularly those based on atom interferometry, are heralding a new era of strategic and robust space exploration. The unique conditions of space, characterized by low noise and low gravity environments, open up diverse possibilities for applications ranging from precise time and frequency transfer to Earth Observation and the search of new Physics. In this paper, we summarise the M-class mission proposal in response to the 2022 call in ESA's science program: Space-Time Explorer and Quantum Equivalence Principle Space Test (STE-QUEST). It consists in a satellite mission featuring a dual-species atom interferometer operating over extended durations. This mission aims to tackle three of the most fundamental questions in Physics: (i) testing the universality of free fall with an accuracy better than one part in $10^{-17}$, (ii) exploring various forms of Ultra-Light Dark Matter, and (iii) scrutinizing the foundations of Quantum Mechanics.

physics.space-ph↗

arXiv2025

Efficient Massive Black Hole Binary parameter estimation for LISA using Sequential Neural Likelihood

The inspiral, merger, and ringdown of Massive Black Hole Binaries (MBHBs) is one the main sources of Gravitational Waves (GWs) for the future Laser Interferometer Space Antenna (LISA), an ESA-led mission in the implementation phase. It is expected that LISA will detect these systems throughout the entire observable universe. Robust and efficient data analysis algorithms are necessary to detect and estimate physical parameters for these systems. In this work, we explore the application of Sequential Neural Likelihood, a simulation-based inference algorithm, to detect and characterize MBHB GW signals in synthetic LISA data. We describe in detail the different elements of the method, their performance and possible alternatives that can be used to enhance the performance. Instead of sampling from the conventional likelihood function, which requires a forward simulation for each evaluation, this method constructs a surrogate likelihood that is ultimately described by a neural network trained from a dataset of simulations of the MBHB signals and noise. One important advantage of this method is that, given that the likelihood is independent of the priors, we can iteratively train models that target specific observations in a fraction of the time and computational cost that other traditional and machine learning-based strategies would require. Because of the iterative nature of the method, we are able to train models to obtain qualitatively similar posteriors with less than 2\% of the simulator calls that Markov Chain Monte Carlo methods would require. We compare these posteriors with those obtained from Markov Chain Monte Carlo techniques and discuss the differences that appear, in particular in relation with the important role that data compression has in the modular implementation of the method that we present. We also discuss different strategies to improve the performance of the algorithms.

gr-qc↗

arXiv2024

Integrability in Perturbed Black Holes: Background Hidden Structures

In this work we investigate the presence of integrable hidden structures in the dynamics of perturbed non-rotating black holes (BHs). This can also be considered as a first step in a wider program of an effective identification of ``slow'' and ``fast'' degrees of freedom (DoFs) in the (binary) BH dynamics, following a wave-mean flow perspective. The slow DoFs would be associated with a nonlinear integrable dynamics, on which the fast ones propagate following an effective linear dynamics. BH perturbation theory offers a natural ground to test these properties. Indeed, the decoupling of Einstein equations into wave master equations with a potential provides an instance of such splitting into (frozen) slow DoFs (background potential) over which the linear dynamics of the fast ones (perturbation master functions) evolve. It has been recently shown that these wave equations possess an infinite number of symmetries that correspond to the flow of the infinite hierarchy of Korteweg-de Vries (KdV) equations. Starting from these results, we systematically investigate the presence of integrable structures in BH perturbation theory. We first study them in Cauchy slices and then extend the analysis to hyperboloidal foliations. This second step introduces a splitting of the master equation into bulk and boundary contributions, unveiling an underlying structural relation with the slow and fast DoFs. This insight represents a first step to establish the integrable structures associated to the slow DoFs as bulk symmetries of the dynamics of perturbed BHs.

gr-qc↗

arXiv2024

Testing gravity with Extreme-Mass-Ratio Inspirals

Extreme-mass-ratio inspirals consist of binary systems of compact objects, with orders of magnitude differences in their masses, in the regime where the dynamics are driven by gravitational wave emission. The unique nature of extreme-mass-ratio inspirals facilitates the exploration of diverse and stimulating tests related to various aspects of black holes and General Relativity. These tests encompass investigations into the spacetime geometry, the dissipation of the binary system energy and angular momentum, and the impact of the intrinsic non-linear effects of the gravitational interaction. This review accounts for the manifold opportunities for testing General Relativity, ranging from examinations of black hole properties to cosmological and multimessenger tests.

gr-qc↗

arXiv2024

Gauge-Independent Metric Reconstruction of Perturbations of Vacuum Spherically-Symmetric Spacetimes

Perturbation theory of vacuum spherically-symmetric spacetimes (including the cosmological constant) has greatly contributed to the understanding of black holes, relativistic compact stars and even inhomogeneous cosmological models. The perturbative equations can be decoupled in terms of (gauge-invariant) master functions satisfying $1+1$ wave equations. In this work, building on previous work on the structure of the space of master functions and equations, we study the reconstruction of the metric perturbations in terms of the master functions. To that end, we consider the general situation in which the perturbations are driven by an arbitrary energy-momentum tensor. Then, we perform the metric reconstruction in a completely general perturbative gauge. In doing so, we investigate the role of Darboux transformations and Darboux covariance, responsible for the isospectrality between odd and even parity in the absence of matter sources and also of the physical equivalence between the descriptions based on all the possible master equations. We also show that the metric reconstruction can be carried out in terms of any of the possible master functions and that the expressions admit an explicitly covariant form.

gr-qc↗

arXiv2023

Universality in Binary Black Hole Dynamics: An Integrability Conjecture

The waveform of a binary black hole coalescence appears to be both simple and universal. In this essay we argue that the dynamics should admit a separation into 'fast and slow' degrees of freedom, such that the latter are described by an integrable system of equations, accounting for the simplicity and universality of the waveform. Given that Painlevé transcendents are a smoking gun of integrable structures, we propose the Painlevé-II transcendent as the key structural element threading a hierarchy of asymptotic models aiming at capturing different (effective) layers in the dynamics. Ward's conjecture relating integrable and (anti)self-dual solutions can provide the avenue to encode background binary black hole data in (non-local) twistor structures.

gr-qc↗

arXiv2023

Black Hole Greybody Factors from Korteweg-de Vries Integrals: Computation

It has recently been shown that the dynamics of perturbed non-rotating black holes (BHs) admits an infinite number of symmetries that are generated by the flow of the Korteweg-de Vries (KdV) equation. These symmetries lead to an infinite number of conserved quantities that can be obtained as integrals of differential polynomials in the potential appearing in the gauge-invariant master equations describing the BH perturbations, the KdV integrals. These conserved quantities are the same for all the possible potentials, which means that they are invariant under Darboux transformations, and they fully determine the BHs transmission amplitudes, or greybody factors, via a moment problem. In this paper we introduce a new semi-analytical method to obtain the greybody factors associated with BH scattering processes by solving the moment problem using only the KdV integrals. The method is based on the use of Padé approximants and we check it first by comparing with results from the case of a Pöschl-Teller potential, for which we have analytical expressions for the greybody factors. Then, we apply it to the case of a Schwarzschild BH and compare with results from computations based on the Wentzel-Kramers-Brillouin (WKB) approximation. It turns out that the new method provides accurate results for the BH greybody factors for all frequencies. The method is also computationally very efficient.

gr-qc↗

arXiv2022

Black Hole Greybody Factors from Korteweg-de Vries Integrals: Theory

The dynamics of perturbed non-rotating black holes (BHs) can be described in terms of master equations of the wave type with a potential. In the frequency domain, the master equations become time-independent Schrödinger equations with no discrete spectrum. It has been recently shown that these wave equations possess an infinite number of symmetries that correspond to the flow of the infinite hierarchy of Korteweg-de Vries (KdV) equations. As a consequence, the infinite set of associated conserved quantities, the KdV integrals, are the same for all the different master equations that we can consider. In this paper we show that the BH scattering reflection and transmission coefficients characterizing the continuous spectrum can be fully determined via a moment problem, in such a way that the KdV integrals provide the momenta of a distribution function depending only on the reflection coefficient. We also discuss the existence and uniqueness of solutions, strategies to solve the moment problem, and finally show the case of the Pöschl-Teller potential where all the steps can be carried out analytically.

gr-qc↗