arXiv subjects

Alexandre M. Pombo

Publications and source records attributed to Alexandre M. Pombo.

At least 19 recordsLinked to original sources

arXiv2026

Coupled by Design: Computing Kerr-Newman Quasinormal Modes with a Hybrid SpectralPINN Solver

We extend our \texttt{SpectralPINN} solver to the computation of Kerr-Newman quasinormal modes by applying it to solve the system of two coupled master PDEs -- advancing from the single, separable equation of the uncharged Kerr limit to a genuinely coupled two-field problem. The coupling between the gravitational and electromagnetic fields gives rise to two families of solutions: the photon-sphere, connecting with Kerr; and near-horizon, disconnected from the Kerr limit, each with two branches of solutions depending on the leading field: the gravitational- and vector-led. Benchmarking against publicly available datasets shows relative frequency errors of $\sim 10^{-4}$ worst case and $\sim10^{-7}$ for most cases. The computed public dataset spans five photon-sphere modes, both gravitational- and vector-led, up to $\ell=4$, as well as two fundamental gravitational-led near-horizon modes. The vector-led photon-sphere branch is computed and systematically characterized for the first time. We apply the dataset and observe the onset of the eigenvalue repulsion reported by Dias \textit{et al.}, to exclude an inter-polarization repulsion within the resolved domain, and to forecast Einstein Telescope constraints on the black-hole charge-to-mass ratio.

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arXiv2025

Teukolsky by Design: A Hybrid Spectral-PINN solver for Kerr Quasinormal Modes

We introduce SpectralPINN, a hybrid pseudo-spectral/physics-informed neural network (PINN) solver for Kerr quasinormal modes that targets the Teukolsky equation in both the separated (radial/angular) and joint two-dimensional formulations. The solver replaces standard neural activation functions with Chebyshev polynomials of the first kind and supports both soft -- via loss penalties -- and hard -- enforced by analytic masks -- implementations of Leaver's normalization. Benchmarking against Leaver's continued-fraction method shows cumulative (real+imaginary part) relative frequency errors of $\sim 0.001\%$ for the separated formulation with hard normalization, $\sim 0.1\%$ for both the soft separated and soft joint formulations, and $\sim 0.01\%$ for the hard joint case. Exploiting our ability to solve the joint equation, we add a small quadrupolar perturbation to the Teukolsky operator, effectively rendering the problem non-separable. The resulting perturbed quasinormal modes are compared against the expected precision of the Einstein Telescope, allowing us to constrain the magnitude of the perturbation. These proof-of-concept results demonstrate that hybrid spectral-PINN solvers can provide a flexible pathway to quasinormal spectra in settings where separability, asymptotics, or field content become more intricate and high accuracy is required.

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arXiv2025

$Q$-balls, neural networks and galaxy rotation curves

Can a dynamically robust (\textit{aka} stable) $Q$-ball reproduce the rotation curve of a disk galaxy? In an astrophysical environment, $Q$-balls are non-topological solitons that are transparent and only perceived by their gravitational effects. Traditionally, scalar $Q$-balls are modelled with a polynomial potential, but axion-like periodic potentials are also expected to support such solitonic configurations. In the presence of angular momentum, $Q$-balls acquire a toroidal structure with a central density void, qualitatively resembling the axially-symmetric structure of disk galaxies. Motivated by this similarity, we investigate whether rotating scalar $Q$-balls can reproduce the observed rotation curves of disk galaxies. In this work, we use a recently developed hybrid numerical framework that combines a high-accuracy pseudo-spectral method with a physics-informed neural network approach to construct both static and rotating $Q$-ball solutions. We assess their ability to act as the dark matter halos in galaxies by fitting the observed rotation curves of a sample of disk galaxies from the SPARC catalogue. Our simplified model provides an overall good agreement with observational data, and a reasonable fit when compared to standard dark matter profiles such as the Navarro-Frenk-White; we have further found an average constraint on the scalar field particle's mass $m\sim 10^{-27}$ eV, in agreement with similar galactic-scale soliton solutions.

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arXiv2025

Black holes and solitonic objects with bosonic fields

Black holes (BH) are among the most unusual and exciting physical objects. Besides being simultaneously Relativistic and quantum mechanical objects, which allows the discovery and/or tests of new physics, BHs also present a lack of "individuality". As a recall, if two stars have the same mass M and angular momentum J, nothing binds them to be distributed in the same way in both stars. However, two distinctly originated BH with the same M and J, will be indistinguishable. In recent years, several alternative models of ultra-compact objects have emerged to explain the unknown Universe. Between them, objects made and/or surrounded by bosonic fields are at the centre of recent developments. This thesis aims to construct and study such bosonic objects. In particular, the scalarization phenomena - where a BH gets immersed in a non-trivial scalar field - and the construction of Boson Stars - self-gravitating configurations of bosonic fields; as well as techniques to study them, namely: decomposition into spherical harmonics and the "complete" study of the virial identity through Derrick's argument. In this regard, we have constructed a parallelized, adaptative-step 6(5) order Runge-Kutta integrator to solve, with very high accuracy, the set of ODEs. Concerning PDEs, we resort to a professional solver (CADSOL/FIDISOL program package) due to the added complexity.

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arXiv2024

The shape of the Chameleon fifth-force on the mass components of galaxy clusters

In the context of Chameleon gravity, we present a semi-analytical solution of the chameleon field profile in accurately modelled galaxy cluster's mass components, namely: the stellar mass of the Brightest Cluster Galaxy (BCG), the baryonic mass in galaxies (other than the BCG), the mass of the Intra-Cluster Medium (ICM) and the diffuse cold dark matter (CDM). The obtained semi-analytic profile is validated against the numerical solution of the chameleon field equation and implemented in the \textsc{MG-MAMPOSSt} code for kinematic analyses of galaxy clusters in modified gravity scenarios. By means of mock halos, simulated both in GR and in modified gravity, we show that the combination of velocities and positions of cluster member galaxies, along with data of the stellar velocity dispersion profile of the BCG, can impose constraints on the parameter space of the Chameleon model; for a cluster generated in GR, these constraints are at the same level as a joint lensing+kinematics analysis of a cluster modelled with a single mass profile, without the BCG data.

astro-ph.CO↗

arXiv2024

Mass Modeling and Kinematics of Galaxy Clusters in Modified Gravity

The chameleon screening mechanism has been constrained many a time using dynamic and kinematic galaxy cluster observables. Current constraints are, however, insensitive to different mass components within galaxy clusters and have been mainly focused on a single mass density profile, the Navarro-Frenk-While mass density model. In this work, we extend the study of the Chameleon screening mechanism in galaxy clusters by considering a series of mass density models, namely: generalized-Navarro-Frenk-While, b-Navarro-Frenk-While, Burket, Isothermal and Einasto. The coupling strength ($\beta$) and asymptotic value of the chameleon field ($\phi_\infty$) are constrained by using kinematics analyses of simulated galaxy clusters, generated both assuming General Relativity and a strong chameleon scenario. By implementing a Bayesian analysis we comprehensively show that the biases introduced due to an incorrect assumption of the mass model are minimal. Similarly, we also demonstrate that a spurious detection of evidence for modifications to gravity is highly unlikely when utilizing the kinematics of galaxy clusters.

astro-ph.CO↗

arXiv2024

Virial identities across the spacetime

Virial-like identities obtained through Derrick's scaling argument are powerful, multi-purpose tools to study general relativistic models. Applications comprise establishing no-go/hair theorems and numerical accuracy tests. In the presence of a horizon (\textit{aka} boundary), the spacetime can be divided into regions, each with its own identity. So far, such identities have only been computed in the region outside the event horizon; however, adding a positive cosmological constant endows an additional boundary (the cosmological horizon), with the region between the latter and the former of particular interest. In this letter, by performing a radial coordinate transformation, we generalise Derrick's scaling argument to compute virial identities \textit{across the whole} non-asymptotically flat spacetimes. The developed method is applied to the entire Reissner-Nordstrom-de Sitter spacetime. A convenient gauge that trivialises the gravitational contribution to the identity between horizons is also found.

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arXiv2023

Mixed scalarization of charged black holes: from spontaneous to non-linear scalarization

Scalarized black holes (BH) have been shown to form dynamically in extended-scalar-tensor theories, either through spontaneous scalarization -- when the BH is unstable against linear perturbations -- or through a non-linear scalarization. In the latter, linearly stable BHs can ignite scalarization when sufficiently perturbed. These phenomena are, however, not incompatible and mixed scalarization is also possible. We explore two aspects of the Einstein-Maxwell-Scalar model: solutions containing, simultaneously, linear (\textit{aka} standard) and non-linear scalarization; and the effects of having one of the coupling constants with an 'opposite sign' to the one leading to scalarization. Both points are addressed by constructing and examining the mixed scalarization's domain of existence. An overall dominance of the spontaneous scalarization over the non-linear scalarization is observed. Thermodynamically, an entropical preference for mixed over the standard scalarization (spontaneous or non-linear) exists. In the presence of counter scalarization, a quench of the scalarization occurs, mimicking the effect of a scalar particle's mass/positive self-interaction term.

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arXiv2023

The spooky ghost of vectorization

An interesting mechanism for the formation of hairy black holes occurs when a vector field, non-minimally coupled to a source term, grows from a perturbation of the vacuum black hole, \textit{aka} vectorization. Its study has, however, been lacking, in part due to the constant threat of ghost instabilities that have plagued vector fields. In this work, we show evidence that, in a generic family of extended-vector-tensor theories where the vector field is non-minimally coupled to the model's invariant (source term), a spherically symmetric, vectorized black hole always suffers from ghost instabilities. These ultimately turn the process of vectorization astrophysically unviable.

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arXiv2023

Effects of mass and self-interaction on nonlinear scalarization of scalar-Gauss-Bonnet black holes

It was recently found that in certain flavours of scalar-Gauss-Bonnet gravity linearly stable bald black holes can co-exist with stable scalarized solutions. The transition between both can be ignited by a large nonlinear perturbation, thus the process was dubbed non-linear scalarization, and it happens with a jump that leads to interesting astrophysical implications. Generalizing these results to the case of nonzero scalar field potential is important because a massive self-interacting scalar field can have interesting theoretical and observational consequences, e.g. reconcile scalar-Gauss-Bonnet gravity with binary pulsar observation, stabilize black hole solutions, etc. That is why in the present paper, we address this open problem. We pay special attention to the influence of a scalar field mass and self-interaction on the existence of scalarized phases and the presence of a jump between stable bald and hairy back holes. Our results show that both the addition of a mass and positive self-interaction of the scalar field result in suppression or quenching of the overall scalarization phenomena. A negative scalar field self-interaction results in an increase of the scalarization. The presence and the size of the jump, though, are not so sensitive to the scalar field potential.

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arXiv2023

Scalaroca stars: coupled scalar-Proca solitons

We construct and explore the physical properties of \textit{scalaroca stars}: spherically symmetric solitonic solutions made of a complex scalar field $Φ$ and a complex Proca field $A^μ$. We restrict our attention to configurations in which both fields are in the fundamental state and possess an equal mass, focusing on the cases when ($i$) the scalar and Proca fields are (non--linearly) super--imposed and do not interact with each other; and ($ii$) the scalar and Proca fields interact through the term $α|Φ| ^2 A^μA_μ$. The solutions are found numerically for the non--interacting case ($α=0$) as well as for both signs of the interaction coupling constant $α$. While pure ($i.e.$ single--field) Proca/scalar boson stars are the most/least massive for weakly--interacting fields, one can obtain more massive solutions for a sufficiently strong interaction. Besides, in the latter case, solutions can be either in a synchronized state -- in which both fields have the same frequency -- or in a non--synchronized state. In addition, we observe that the coupling between the two fields allows solitonic solutions with a real scalar field. We further comment on the possibility of spontaneous scalarization and vectorization of the interacting solitonic solution.

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arXiv2023

A Sun-like star orbiting a boson star

The high-precision astrometric mission GAIA recently reported the remarkable discovery of a Sun-like star closely orbiting a dark object, with a semi-major axis and period of $1.4\, \rm{AU}$ and $187.8$ days respectively. While the plausible expectation for the central dark object is a black hole, the evolutionary mechanism leading to the formation of such a two-body system is highly challenging. Here, we challenge the scenario of a central black hole and show that the observed orbital dynamics can be explained under fairly general assumptions if the central dark object is a stable clump of bosonic particles of spin-0, or spin-1, known as a boson star. We further explain how future astrometric measurements of similar systems will provide an exciting opportunity to probe the fundamental nature of compact objects and test compact alternatives to black holes.

astro-ph.SR↗

arXiv2022

A convenient gauge for virial identities in axial symmetry

Virial identities are a useful mathematical tool in General Relativity. Not only have they been used as a numerical accuracy tool, but they have also played a significant role in establishing no-go and no-hair theorems while giving some physical insight into the considered system from an energy balance perspective. While the calculation of these identities tends to be a straightforward application of Derrick's scaling argument~\cite{derrick1964comments}, the complexity of the resulting identity is system dependent. In particular, the contribution of the Einstein-Hilbert action, due to the presence of second-order derivatives of the metric functions, becomes increasingly complex for generic metrics. Additionally, the Gibbons-Hawking-York term needs to be taken into account \cite{Herdeiro:2021teo}. Thankfully, since the gravitational action only depends on the metric, it is expected that a ``convenient'' gauge that trivializes the gravitational action contribution exists. While in spherical symmetry such a gauge is known (the $m-σ$ parametrization), such has not been found for axial symmetry. In this letter, we propose a ``convenient'' gauge for axial symmetry and use it to compute an identity for Kerr black holes with scalar hair.

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arXiv2022

Deconstructing scaling virial identities in General Relativity: spherical symmetry and beyond

Derrick-type virial identities, obtained via dilatation (scaling) arguments, have a variety of applications in field theories. We deconstruct such virial identities in relativistic gravity showing how they can be recast as self-evident integrals of appropriate combinations of the equations of motion. In spherical symmetry, the appropriate combination and gauge choice guarantee the geometric part can be integrated out to yield a master form of the virial identity as a non-trivial energy-momentum balance condition, valid for both asymptotically flat black holes and self-gravitating solitons, for any matter model. Specifying the matter model we recover previous results obtained via the scaling procedure. We then discuss the more general case of stationary, axi-symmetric, asymptotically flat black hole or solitonic solutions in General Relativity, for which a master form for their virial identity is proposed, in a specific gauge but regardless of the matter content. In the flat spacetime limit, the master virial identity for both the spherical and axial cases reduces to a balance condition for the principal pressures, discussed by Deser.

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arXiv2021

Aspects of Gauss-Bonnet scalarisation of charged black holes

The general relativity vacuum black holes (BHs) can be scalarised in models where a scalar field non-minimally couples to the Gauss-Bonnet (GB) invariant. Such GB scalarisation comes in two flavours, depending on the GB sign that triggers the phenomenon. Hereafter these two cases are termed GB$^\pm$ scalarisation. For vacuum BHs, only GB$^+$ scalarisation is possible in the static case, while GB$^-$ scalarisation is $spin$ induced. But for electrovacuum BHs, GB$^-$ is also $charged$ induced. We discuss the GB$^-$ scalarisation of Reissner-Nordström and Kerr-Newman BHs, discussing zero modes and constructing fully non-linear solutions. Some comparisons with GB$^+$ scalarisation are given. To assess the generality of the observed features, we also briefly consider the GB$^\pm$ scalarisation of stringy dilatonic BHs and coloured BHs which provide qualitative differences with respect to the electrovacuum case.

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arXiv2021

Virial identities in relativistic gravity: 1D effective actions and the role of boundary terms

Virial (aka scaling) identities are integral identities that are useful for a variety of purposes in non-linear field theories, including establishing no-go theorems for solitonic and black hole solutions, as well as for checking the accuracy of numerical solutions. In this paper, we provide a pedagogical rationale for the derivation of such integral identities, starting from the standard variational treatment of particle mechanics. In the framework of one-dimensional (1D) effective actions, the treatment presented here yields a set of useful formulas for computing virial identities in any field theory. Then, we propose that a complete treatment of virial identities in relativistic gravity must take into account the appropriate boundary term. For General Relativity this is the Gibbons-Hawking-York boundary term. We test and confirm this proposal with concrete examples. Our analysis here is restricted to spherically symmetric configurations, which yield 1D effective actions (leaving higher-D effective actions and in particular the axially symmetric case to a companion paper). In this case, we show that there is a particular "gauge" choice, $i.e.$ a choice of coordinates and parameterizing metric functions, that simplifies the computation of virial identities in General Relativity, making both the Einstein-Hilbert action and the Gibbons-Hawking-York boundary term non-contributing. Under this choice, the virial identity results exclusively from the matter action. For generic "gauge" choices, however, this is not the case.

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arXiv2021

The imitation game: Proca stars that can mimic the Schwarzschild shadow

Can a dynamically robust bosonic star (BS) produce an (effective) shadow that mimics that of a black hole (BH)? The BH shadow is linked to the existence of light rings (LRs). For free bosonic fields, yielding mini-BSs, it is known that these stars can become ultra-compact - i.e., possess LRs - but only for perturbatively unstable solutions. We show this remains the case even when different self-interactions are considered. However, an effective shadow can arise in a different way: if BSs reproduce the existence of an innermost stable circular orbit (ISCO) for timelike geodesics (located at $r_{\rm ISCO}=6M$ for a Schwarzschild BH of mass M), the accretion flow morphology around BHs is mimicked and an effective shadow arises in an astrophysical environment. Even though spherical BSs may accommodate stable timelike circular orbits all the way down to their centre, we show the angular velocity along such orbits may have a maximum away from the origin, at $R_Ω$; this scale was recently observed to mimic the BH's ISCO in some scenarios of accretion flow. Then: (i) for free scalar fields or with quartic self-interactions, $R_Ω\neq 0$ only for perturbatively unstable BSs; (ii) for higher scalar self-interactions, e.g. axionic, $R_Ω\neq 0$ is possible for perturbatively stable BSs, but no solution with $R_Ω=6M$ was found in the parameter space explored; (iii) but for free vector fields, yielding Proca stars (PSs), perturbatively stable solutions with $R_Ω\neq 0$ exist, and indeed $R_Ω=6M$ for a particular solution. Thus, dynamically robust spherical PSs can mimic the shadow of a (near-)equilibrium Schwarzschild BH with the same M, in an astrophysical environment, despite the absence of a LR, at least under some observation conditions, as we confirm by comparing the lensing of such PSs and Schwarzschild BHs.

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arXiv2020

Spontaneous vectorization of electrically charged black holes

In this work, we generalise the spontaneous scalarization phenomena in Einstein-Maxwell-Scalar models to a higher spin field. The result is an Einstein-Maxwell-Vector model wherein a vector field is non-minimally coupled to the Maxwell invariant by an exponential coupling function. We show that the latter guarantees the circumvention of an associated no-hair theorem when the vector field has the form of an electric field. Different than its scalar counterpart, the new spontaneously vectorized Reissner-Nordström (RN) black holes are, always, undercharged while being entropically preferable. The solution profile and domain of existence are presented and analysed.

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