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Etevaldo dos Santos Costa Filho

Publications and source records attributed to Etevaldo dos Santos Costa Filho.

16 recordsLinked to original sources
arXiv2026

Boson Star Factory: Past, Present, and Future

Boson stars are self-gravitating solitons of the Einstein-Klein-Gordon equations for a massive complex scalar field, and arguably the simplest horizonless compact objects arising in General Relativity. Beyond spherical symmetry, their construction requires solving a system of nonlinear elliptic partial differential equations, a difficult task per se and that each group has traditionally addressed with its own numerical implementation. A systematic comparison of different methods applied to the same physical model has so far been lacking. In this work, we carry out such a comparison for the two simplest non-spherical configurations: rotating boson stars and static dipolar boson stars. We employ three independent codes, based respectively on finite differences (FIDISOL/CADSOL), finite elements (FreeFem), and spectral methods (Kadath), and assess their accuracy through different diagnostics. The three solvers agree on the global observables to typically eight significant digits. We further compare the runtime of each code on identical hardware and provide precise benchmark values of the relevant physical quantities, intended to serve as reference data for future numerical studies of boson stars. As a further proof of concept, we also present the use of physics-informed neural networks to construct a rotating Q-ball solution.

gr-qc↗
arXiv2026

Bosonic stars with dark electroweak fields

We construct bosonic stars in the Einstein-Weinberg-Salam theory, namely the bosonic sector of the electroweak Standard Model minimally coupled to Einstein's theory of gravity. These configurations are everywhere regular, spherically symmetric and asymptotically flat, consisting of a static condensate of the massive $W$ and $Z$ bosons, whose masses arise from the Higgs mechanism. Although the corresponding fields exist in nature, gravitational effects are negligible at the physical electroweak scale and the configurations would be microscopic. Keeping Newton's constant and the electroweak mass ratios at their physical values, we therefore interpret the model as the bosonic sector of a \textit{dark} electroweak theory with a radically different energy scale. Choosing the ultralight vector boson mass $m_{\mathrm{W}}c^{2}=8.7\times10^{-13}\,$eV, as suggested by the Proca star interpretation of GW190521, our bosonic stars can attain masses in the intermediate-mass black hole range.

gr-qc↗
arXiv2026

Test-particle dynamics in a noncommutative deformation of Einstein-Rosen waves

We investigate phenomenological effects induced by a noncommutative deformation of Einstein--Rosen gravitational-waves within the framework of the Riemannian geometry of noncommutative surfaces developed by Chaichian et al. Considering a noncommutative structure between the radial and axial coordinates, we study perturbatively the motion of nonrelativistic test particles in the corresponding deformed geometry. We show that the deformation generates a coupling between the radial and longitudinal sectors, while the radial dynamics remains unaffected by the noncommutative deformation at the perturbative order considered. The induced longitudinal response is governed by a spectrally weighted functional of the gravitational-wave profile, implying that longitudinal observables depend on higher-order spectral moments than their commutative radial counterparts. As a consequence, noncommutative effects exhibit enhanced sensitivity to the ultraviolet structure of the gravitational configuration. We analyze separately monochromatic Einstein--Rosen waves and the localized Weber--Wheeler pulse. In the monochromatic case, the noncommutative correction induces a quasi-periodic longitudinal motion, whereas for the Weber--Wheeler pulse it produces an impulsive longitudinal response analogous to a gravitational velocity memory effect. In addition, we derive an explicit analytical expression in commutative General Relativity for the residual radial velocity generated by the Weber--Wheeler pulse at large radial distances in the perturbative regime.

gr-qc↗
arXiv2026

From rotating attractors to extremal black holes with axionic hair

We study extremal, rotating black holes in four-dimensional Einstein-Maxwell-axion (EMA) theory through a combined near-horizon and bulk analysis. At the level of the near-horizon extremal geometry (NHEG), using the entropy function formalism, we prove that regular rotating attractors with axionic hair exist only for configurations that are purely electrically or purely magnetically charged; regular rotating dyonic attractors are excluded by the axion equation of motion, a result that we established perturbatively and non-perturbatively within the NHEG system. On the global side, we construct families of asymptotically flat, rotating extremal EMA black holes that interpolate to the electric NHEG branch, confirming that horizon data are fixed by extremization of the entropy function and decoupled from asymptotic moduli in line with the attractor mechanism.

gr-qc↗
arXiv2026

Relativistic and Newtonian Proca Stars: A Tale of Two Limits

We investigate a representative set of static solitonic solutions of the Einstein-Proca theory in the Newtonian regime, where the field frequency approaches the particle mass, $ω\to μ$, and compare them with the corresponding solutions of the spin-1 Schrödinger-Poisson system, which provides the effective description in this limit. While this correspondence is relatively straightforward in the Einstein-Klein-Gordon case, the vector nature of the Proca field, combined with the enhanced $U(3)$ symmetry of the nonrelativistic spin-1 regime, gives rise to several nontrivial features that require careful analysis. We establish a mapping between the two descriptions by identifying $\ell=0$ electric Proca stars with radially polarized (hedgehog) configurations and $\ell=1$ electric Proca stars with linearly polarized configurations. We further clarify some aspects of the ground state and resolve several apparent discrepancies between relativistic and Newtonian solutions, particularly concerning their morphology and stability properties. An important conclusion of this work is that the nonrelativistic regime supports a richer spectrum of stable equilibrium configurations than the relativistic theory, including stable excited states.

gr-qc↗
arXiv2026

Spinning extremal dyonic black holes in $γ=1$ Einstein-Maxwell-dilaton theory

We propose a general framework for the study of asymptotically flat spinning dyonic {\it extremal} black holes (eBHs) in $D=4$ Einstein-Maxwell-dilaton theory. Restricting to the stringy value $γ=1$ of the dilaton coupling constant, we report on the existence of a one parameter family of eBHs which are free of pathologies, provided their magnetic and electric charges are equal. An understanding of this condition is found from a study of the near horizon limit of the solutions, both perturbative closed form and numerical solutions being presented.

gr-qc↗
arXiv2026

Charged, rotating black holes in Einstein-Maxwell-dilaton theory

The asymptotically flat, electrically charged, rotating black holes (BHs) in Einstein-Maxwell-dilaton (EMd) theory are known in closed form for \textit{only} two particular values of the dilaton coupling constant $γ$: the Einstein-Maxwell coupling ($γ=0$), corresponding to the Kerr-Newman (KN) solution, and the Kaluza-Klein coupling ($γ=\sqrt{3}$). Rotating solutions with arbitrary $γ$ are known only in the slow-rotation or weakly charged limits. In this work, we numerically construct such EMd BHs with arbitrary $γ$. We present an overview of the parameter space of the solutions for illustrative values of $γ$ together with a study of their basic properties. The solutions are in general KN-like; there are however, new features. The data suggest that the spinning solutions with $0<γ<\sqrt{3}$ possess a zero temperature limit, which, albeit regular in terms of curvature invariants, exhibits a $pp$-singularity. A different limiting behaviour is found for $γ>\sqrt{3}$, in which case, moreover, we have found hints of BH non-uniqueness for the same global charges.

gr-qc↗
arXiv2026

Multipolar Proca stars: electric, magnetic and hybrid solitons

We construct new families of everywhere regular, asymptotically flat solitons in the Einstein--Proca model, obtained as self-gravitating continuations of flat-spacetime (singular) Proca multipoles. First we consider static and axially symmetric solutions, organized by a multipole number $\ell$. Two distinct classes arise: electric-type configurations, which include the spherical Proca stars as the $\ell=0$ case, and magnetic-type configurations, which have no spherical counterpart and start at $\ell=1$. Then we construct hybrid solutions as nonlinear superpositions of electric and magnetic multipoles. These have non-vanishing local angular momentum density but vanishing total angular momentum, and in some cases have no north-south $\mathbb{Z}_2$-symmetry. By performing dynamical evolutions of Proca stars in the new magnetic and hybrid sectors, we show they are unstable, decaying to the (static) prolate Proca stars or the (stationary) spinning Proca stars, previously identified as dynamically robust, electric sector configurations. In some cases, they can also collapse into a black hole.

gr-qc↗
arXiv2024

Self-interactions can (also) destabilize bosonic stars

We study the dynamical stability of Proca-Higgs stars, in spherical symmetry. These are solutions of the Einstein-Proca-Higgs model, which features a Higgs-like field coupled to a Proca field, both of which minimally coupled to the gravitational field. The corresponding stars can be regarded as Proca stars with self-interactions, while avoiding the hyperbolicity issues of self-interacting Einstein-Proca models. We report that these configurations are stable near the Proca limit in the candidate stable branches, but exhibit instabilities in certain parts of the parameter space, even in the candidate stable branches, regaining their stability for very strong self-interactions. This shows that for these models, unlike various examples of scalar boson stars, self-interactions can deteriorate, rather than improve, the dynamical robustness of bosonic stars.

gr-qc↗
arXiv2024

Universal Relations for Rotating Scalar and Vector Boson Stars

Bosonic stars represent a hypothetical exotic type of compact stellar objects that could be observed from the gravitational signal of coalescing binaries in current and future gravitational wave detectors. There are two main families of bosonic stars, which depend on the nature that governs the particles that build them: Einstein-Klein-Gordon and Proca Stars. We study the multipolar structure for both families of rotating objects, using realistic potentials with the aim of finding possible universal relations and, thus, a method that allows us to distinguish between these and other compact objects in the gravitational wave paradigm. We also show how certain relevant observables can be obtained for these hypothetical but well-motivated astrophysical objects.

gr-qc↗
arXiv2024

Spinning Proca-Higgs balls, stars and hairy black holes

Recently, spherical and static flat space solitons (balls) and self-gravitating, everywhere regular, asymptotically flat solitons (stars) were constructed in an Einstein-Proca-Higgs model [1], where a complex vector field gains mass by coupling to a real scalar field with a Higgs-type potential. The Proca-Higgs model serves as a UV completion of a complex Proca model with self-interactions. Here, we construct and examine the mathematical and physical properties of rotating configurations. In particular, rotation allows horizon-bearing solutions, including stationary clouds surrounding Kerr black holes and their non-linear continuation into black holes with Proca-Higgs hair.

gr-qc↗
arXiv2023

Proca-Higgs balls and stars in a UV completion for Proca self-interactions

We consider a Proca-Higgs model wherein a complex vector field gains mass via spontaneous symmetry breaking, by coupling to a real scalar field with a Higgs-type potential. This vector version of the scalar Friedberg-Lee-Sirlin model, can be considered as a UV completion of a complex Proca model with self-interactions. We study the flat spacetime and self-gravitating solitons of the model, that we dub Proca-Higgs \textit{balls} and \textit{stars} respectively, exploring the domain of solutions and describing some of their mathematical and physical properties. The stars reduce to the well-known (mini-)Proca stars in some limits. The full model evades the hyperbolicity problems of the self-interacting Proca models, offering novel possibilities for dynamical studies beyond mini-Proca stars.

gr-qc↗
arXiv2021

Collective coordinates for the hybrid model

In the present work, we carry out the study of scattering solitons for the anti-kink/kink and kink/anti-kink configurations. Furthermore, we can observe the same effects as those described by D. Bazeia et al.. We apply the collective coordinate approximation method to describe both scattering configurations and verify that just as happens in the polynomial models $ϕ^4$ and $ϕ^6$, the method has its limitations regarding the initial scattering speeds. In such a way that, for certain initial speeds, the solution of collective coordinates agrees with the fullsimulation, and for other speeds, there is a discrepancy in the solutions obtained by these two methods. We also noticed that, considering the hybrid model, the null-vector problem persists for both configurations, and when trying to fix it, a singularity is created in moduli-space as well as in $ϕ^4$.

hep-th↗
arXiv2020

Calculation of multipole moments of axistationary electrovacuum spacetimes

The multipole moments of stationary axially symmetric vacuum or electrovacuum spacetimes can be expressed in terms of the power series expansion coefficients of the Ernst potential on the axis. In this paper we present a simpler, more efficient calculation of the multipole moments, applying methods introduced by Bäckdahl and Herberthson. For the non-vacuum electromagnetic case, our results for the octupole and higher moments differ from the results already published in the literature. The reason for this difference is that we correct an earlier unnoticed mistake in the power series solution of the Ernst equations. We also apply the presented method to directly calculate the multipole moments of a 5-parameter charged magnetized generalization of the Kerr and Tomimatsu-Sato exact solutions.

gr-qc↗
arXiv2020

Corotating binary systems of identical Kerr-Newman black holes

In the present paper binary configurations of identical corotating Kerr-Newman black holes separated by a massless strut are derived and studied. After solving the axis conditions and establishing the absence of magnetic charges in the solution, one gets two 4-parametric corotating binary black hole models endowed with electric charge, where each source contains equal/opposite electric charge in the first/second configuration. Since the black hole horizons are given by concise expressions in terms of physical parameters, all their thermodynamical properties satisfying the Smarr relation for the mass are also obtained. We discuss the physical limits of both models.

gr-qc↗