arXiv subjects

Miguel Alcubierre

Publications and source records attributed to Miguel Alcubierre.

At least 19 recordsLinked to original sources

arXiv2026

Charged Dirac stars

In this work we solve the coupled Einstein-Dirac-Maxwell (EDM) system for static spherically symmetric configurations of two fermions in a singlet spinor state within the $3+1$ formalism of general relativity. We find different families of stationary self-gravitating solutions for the Dirac field through a numerical shooting method for different values of the electric charge parameter q. Furthermore, we investigate the effect of the charge q on the binding energy, mass, radius, and compactness of the solutions. We show that gravitationally bound configurations exist only for $q m$, we find that they are always gravitationally unbound.

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arXiv2026

Noble gravitational atoms: Self-gravitating black hole scalar wigs with angular momentum number

We present new spherically symmetric solutions of the Einstein-Klein-Gordon equations in a quasi-stationary approximation that describe self-gravitating scalar field configurations around a black hole, including angular momentum number $\ell$. An approach analogous to the one which gives rise to $\ell$-boson stars is used here to construct self-gravitating ``gravitational atoms" with $\ell\ge0$. We refer to these new solutions as {\it noble gravitational atoms}, by analogy with noble atoms, which are characterized by closed electron shells. We show that, in the proper limit, noble gravitational atoms approach $\ell$-boson stars globally, displaying noticeable differences only in a region very close to the event horizon. Noble gravitational atoms with $\ell>0$ sometimes present density maxima located at relatively large radii, with small density close to the horizon for $\ell>1$. Furthermore, they do not always present the typical density spike at the event horizon if $\ell > 0$; on the contrary, they sometimes exhibit a small dip there. When $\ell=0$, a spike can appear, but its contribution to the total mass density is always negligible. The size, density, and lifetime of these objects vary significantly depending on the parameters, being in some cases as large as galaxies, as dilute as dark matter, and as long-lived as the Universe itself.

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arXiv2026

Dynamical Evolutions of Electrically Charged Proca Stars

In a previous work we constructed different families of stationary electrically charged Proca stars characterized by a charge parameter $q$, by solving the Einstein--Maxwell--Proca system in spherical symmetry, and imposing a harmonic time dependence ansatz for the Proca field (Mio and Alcubierre, 2025). We showed that there is a critical value for the charge $q_c$ that corresponds to the value for which the Coulomb repulsion of the charged Proca field exactly cancels the Newtonian gravitational attraction, and we found that supercritical solutions can only exist for a limited range of charges above this critical value $q>q_c$. Here we study the dynamical stability properties of these charged Proca stars by adding a small but finite perturbation to the original stationary configurations, and then performing numerical evolutions while keeping the spherical symmetry. We show that, for any given family, the parameter space can be separated into three regions corresponding to gravitationally bound stable configurations, gravitationally bound unstable configurations, and gravitationally unbound unstable configurations. For the unstable configurations we follow the evolution in time in order to determine their final state, and find that this final state can be collapse to a charged Reissner--Nordstrom black hole, migration to a new state in the stable branch, or dispersion to infinity, depending on the value of the binding energy and the specific form of the perturbation.

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arXiv2026

A natural explanation of the Galactic Magnetic Fields from multistate Scalar Field Dark Matter

In this article, we investigate the possibility that the large-scale magnetic fields observed in galaxies, of the order of microgauss, arise naturally from a complex Scalar Field Dark Matter (SFDM) halo charged under a local $U(1)$ symmetry. Extending our previous work, where multistate SFDM solutions were shown to form ``gravitational atoms'' capable of explaining the anisotropic distribution of satellite galaxies (VPOS), we analyze here the coupled dynamics of the scalar and a gauge field at the perturbative level. By solving the perturbed Klein-Gordon and gauge-field equations, we find the temporal evolution and show that the spatial structure of the induced electromagnetic fields is governed by the same spherical Bessel functions and spherical harmonics that characterize the ground and excited states of the multi-state SFDM halo. Remarkably, the presence of the gauge field does not modify the dark-matter density distribution, which preserves the multi-state configuration previously obtained. Our results demonstrate that a charged multi-state SFDM halo can generate coherent, large-scale magnetic fields whose morphology is determined by the excited modes of the scalar field, providing a unified framework in which both galactic magnetic fields and VPOS-like structures originate from the underlying quantum nature of dark matter.

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arXiv2025

Electrically Charged Proca Stars

We consider self-gravitating stationary configurations of a charged massive complex Proca field, also known as charged Proca stars, in the particular case of spherical symmetry. We first present a general 3+1 decomposition of the Einstein--Maxwell--Proca system, starting from the action and field equations. We then restrict our system to the case of spherical symmetry and, after imposing a harmonic time dependence ansatz for the Proca field, we construct families of charged Proca stars for different values of the charge parameter $q$, and different values of the central Proca scalar potential $φ$. In a similar way to the case of scalar boson stars, one can define a critical charge $q=q_c$ that corresponds to the value for which the Coulomb repulsion of the charged Proca field exactly cancels their newtonian gravitational attraction. We find that supercritical solutions can exist for a limited range of charges above the critical value $q>q_c$. We also consider the binding energy $E_B$ for the different families of solutions, and find that gravitationally bound solutions such that $E_B<0$ can only exist for subcritical charges such that $q<q_c$, indicating that our supercritical solutions are probably dynamically unstable against perturbations.

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arXiv2025

Non-linear stability analysis of $\ell$-Proca stars

Vector boson stars, also known as Proca stars, exhibit remarkable dynamical robustness, making them strong candidates for potential astrophysical exotic compact objects. In search of theoretically well-motivated Proca star models, we recently introduced the $\ell$-Proca star, a multi-field extension of the spherical Proca star, whose $(2\ell + 1)$ constitutive fields have the same time and radial dependence, and their angular structure is given by all the available spherical harmonics for a fixed angular momentum number $\ell$. In this work, we conduct a non-linear stability analysis of these stars by numerically solving the Einstein-(multi, complex) Proca system for the case of $\ell = 2$, which are formed by five constitutive independent, complex Proca fields with $m = 0, |1|$, and $|2|$. Our analysis is based on long-term, fully non-linear, 3-dimensional numerical-relativity simulations without imposing any symmetry. We find that ($\ell=2$)-Proca stars are unstable throughout their entire domain of existence. In particular, we highlight that less compact configurations dynamically lose their global spherical symmetry, developing a non-axisymmetric $\tilde{m}=4$ mode instability and a subsequent migration into a new kind of multi-field Proca star formed by fields with different angular momentum number, $\ell=1$ and $\ell=2$, that we identify as unstable multi-$\ell$ Proca stars.

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arXiv2025

Gravitational atoms beyond the test field limit: The case of Sgr A* and ultralight dark matter

We construct gravitational atoms including self-gravity, obtaining solutions of the Einstein-Klein-Gordon equations for a scalar field surrounding a non-rotating black hole in a quasi-stationary approximation. We resolve the region near the horizon as well as the far field region. Our results are relevant in a wide range of masses, from ultralight to MeV scalar fields and for black holes ranging from primordial to supermassive. For instance, a system with a scalar field consistent with ultralight dark matter and a black hole mass comparable to that of Sagittarius A* can be modeled. A density spike near the event horizon, although present, is negligible, contrasting with the prediction in [P. Gondolo and Silk, Phys. Rev. Lett., 83:1719-1722, 1999] for cold dark matter.

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arXiv2025

The Dirac equation in General Relativity and the 3+1 formalism

I present a review of the Dirac equation in general relativity. Although the generalization of the Dirac equation to a curved spacetime is well known, it is not usually part of the standard toolkit of techniques known to people working on classical general relativity. Recently, there has been some renewed interest in studying solutions of the Einstein--Dirac system of equations, particularly in the context of the so-called ``Dirac stars''. Motivated by this, here I present a review of the Dirac equation in general relativity, starting from Minkowski spacetime, and then considering the Lorentz group and the tetrad formalism in order to generalize this equation to the case of a curved spacetime. I also derive the form of the Dirac equation and its associated stress--energy tensor for the case of the 3+1 formalism of general relativity, which can be useful for the study of the evolution of the Dirac field in a dynamical spacetime.

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arXiv2025

Proca stars in excited states

In this paper we consider families of solutions for excited states of Proca stars in spherical symmetry. We focus on the first two excited configurations and perform a series of fully non-linear dynamical simulations in order to study their properties and stability. Our analysis reveals that excited Proca stars are always unstable against even very small perturbations, and their dynamical evolution can lead to three different final states: collapse to a black hole, dissipation, or migration to a different configuration in the ground state. We find that migration to the ground state can only occur in a small region of the parameter space of solutions with negative binding energy.

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arXiv2024

Spherically symmetric collapse: Initial configurations

The initial state of the spherical gravitational collapse in general relativity has been studied with different methods, especially by using {\it a priori} given equations of state that describe the matter as a perfect fluid. We propose an alternative approach, in which the energy density of the perfect fluid is given as a polynomial function of the radial coordinate that is well-behaved everywhere inside the fluid. We then solve the corresponding differential equations, including the Tolman-Oppenheimer-Volkoff equilibrium condition, using a fourth-order Runge-Kutta method and obtain a consistent model with a central perfect-fluid core surrounded by dust. We analyze the Hamiltonian constraint, the mass-to-radius relation, the boundary and physical conditions, and the stability and convergence properties of the numerical solutions. The energy density and pressure of the resulting matter distribution satisfy the standard physical conditions. The model is also consistent with the Buchdahl limit and the speed of sound conditions, even by using realistic values of compact astrophysical objects such as neutron stars.

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arXiv2024

$\ell$-Proca stars

Initially applied to the scalar case, we extend the applicability of the multi-field generalization with angular momentum of bosonic stars to the vector case, in order to obtain new configurations that generalize the one-field spherical Proca stars. These new objects, which we call $\ell$-Proca stars, arise as stationary and spherically symmetric bosonic stars solutions of the Einstein-(multi)Proca system, whose matter content is formed by an arbitrary odd number of $2\ell+1$ of complex Proca fields with the same mass, time-frequency, radial profile and angular momentum number $\ell$. We analyze the system of constraint and evolution radial equations for the matter content to show the consistency of our proposal, and obtain numerically the ground states of these new solutions for the first few values of $\ell$ using spectral methods.

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arXiv2023

Charged boson stars revisited

We consider again stationary solutions to the spherically symmetric Einstein--Maxwell--Klein--Gordon system, commonly known as ``charged boson stars'', originally studied by Jetzer and Van Der Bij. We construct families of charged boson stars in the ground state, for different values of the charge parameter $q$, and different values of the central scalar field. Following Jetzer and Van Der Bij, one can define a critical value for the charge $q=q_c$ that corresponds to the value for which the Coulomb repulsion of the bosonic particles exactly cancels their newtonian gravitational attraction. We confirm the claim made by Pugliese et al. that super-critical solutions exist for a limited range of charges above the critical value $q>q_c$ (though we find an even smaller range of $q$ for which this is possible). Our analysis indicates, however, that all such super-critical solutions are gravitationally unbound, and are therefore expected to be unstable. One of the main results of our analysis is the fact that, even though we do find a family of slightly super-critical solutions in the sense that $q>q_c$, there are no super-critical solutions in the sense that the total charge $Q$ is larger than the total mass $M$ of the system.

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arXiv2023

Boson stars and their relatives in semiclassical gravity

We construct boson star configurations in quantum field theory using the semiclassical gravity approximation. Restricting our attention to the static case, we show that the semiclassical Einstein-Klein-Gordon system for a {\it single real quantum} scalar field whose state describes the excitation of $N$ {\it identical particles}, each one corresponding to a given energy level, can be reduced to the Einstein-Klein-Gordon system for $N$ {\it complex classical} scalar fields. Particular consideration is given to the spherically symmetric static scenario, where energy levels are labeled by quantum numbers $n$, $\ell$ and $m$. When all particles are accommodated in the ground state $n=\ell=m=0$, one recovers the standard static boson star solutions, that can be excited if $n\neq 0$. On the other hand, for the case where all particles have fixed radial and total angular momentum numbers $n$ and $\ell$, with $\ell\neq 0$, but are homogeneously distributed with respect to their magnetic number $m$, one obtains the $\ell$-boson stars, whereas when $\ell=m=0$ and $n$ takes multiple values, the multi-state boson star solutions are obtained. Further generalizations of these configurations are presented, including the multi-$\ell$ multi-state boson stars, that constitute the most general solutions to the $N$-particle, static, spherically symmetric, semiclassical real Einstein-Klein-Gordon system, in which the total number of particles is definite. In spite of the fact that the same spacetime configurations also appear in multi-field classical theories, in semiclassical gravity they arise naturally as the quantum fluctuations associated with the state of a single field describing a many-body system. Our results could have potential impact on direct detection experiments in the context of ultralight scalar field/fuzzy dark matter candidates.

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arXiv2022

Critical gravitational collapse of a massive complex scalar field

We study the critical collapse of a massive complex scalar field coupled minimally to gravity. Taking as initial data a simple gaussian pulse with a shape similar to the harmonic ansatz for boson stars, we obtain critical collapse of type type I and II when varying the gaussian width $σ$. For $σ\leq 0.5$ we find collapse of type II with a critical exponent $γ=0.38\pm0.01$ and an echoing period $Δ=3.4\pm0.1$. These values are very similar to the known results for a real massless scalar field. On the other hand, for $σ\geq 2.5$ we obtain collapse of type I. In this case we find that the critical solutions turn out to be an unstable boson stars in the ground state: all the data obtained from our simulations can be contrasted with the characteristic values for unstable boson stars and their corresponding Lyapunov exponents.

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arXiv2022

Extreme $\ell$-boson stars

A new class of complex scalar field objects, which generalize the well known boson stars, was recently found as solutions to the Einstein-Klein-Gordon system. The generalization consists in incorporating some of the effects of angular momentum, while still maintaining the spacetime's spherical symmetry. These new solutions depend on an (integer) angular parameter $\ell$, and hence were named $\ell$-boson stars. Like the standard $\ell=0$ boson stars these configurations admit a stable branch in the solution space; however, contrary to them they have a morphology that presents a shell-like structure with a "hole" in the internal region. In this article we perform a thorough exploration of the parameter space, concentrating particularly on the extreme cases with large values of $\ell$. We show that the shells grow in size with the angular parameter, doing so linearly for large values, with the size growing faster than the thickness. Their mass also increases with $\ell$, but in such a way that their compactness, while also growing monotonically, converges to a finite value corresponding to about one half of the Buchdahl limit for stable configurations. Furthermore, we show that $\ell$-boson stars can be highly anisotropic, with the radial pressure diminishing relative to the tangential pressure for large $\ell$, reducing asymptotically to zero, and with the maximum density also approaching zero. We show that these properties can be understood by analyzing the asymptotic limit $\ell\rightarrow\infty$ of the field equations and their solutions. We also analyze the existence and characteristics of both timelike and null circular orbits, especially for very compact solutions.

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arXiv2021

Critical gravitational collapse of a non-minimally coupled scalar field

We study the critical gravitational collapse of a massless scalar field non-minimally coupled to gravity, using a quadratic coupling function with a strength parameter $ξ$. We concentrate on critical phenomena of type II, and determine with an accuracy of at least $10^{-12}$ the value of the critical amplitude for collapse to a black hole, as well as the values of the critical and echoing exponents. Obtaining such high accuracy in the critical amplitude requires us to do a coordinate radial transformation that effectively increases resolution near the central regions by a factor of at least $10^3$. As expected, we find that for the case of small coupling the critical behaviour is very similar to that of a minimally coupled scalar field. On the other hand, for high coupling the dynamics become so violent that we need to introduce a special slicing condition, known as the shock-avoiding slicing condition, in order to avoid gauge pathologies that would otherwise cause our simulations to fail. With this new gauge condition we are able to perform high accuracy simulations even in the strong coupling regime, where we find that the critical and echoing exponents become significantly smaller, and that the echoing behavior is richer and can not be modelled by a single harmonic.

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arXiv2021

On the linear stability of $\ell$-boson stars with respect to radial perturbations

In previous work we constructed new boson star solutions consisting of a family of massive complex scalar fields minimally coupled to gravity in which the individual fields have angular momentum, yet the configuration as a whole is static and spherically symmetric. In the present article we study the linear stability of these $\ell$-boson stars with respect to time-dependent, radial perturbations. The pulsation equations, governing the dynamics of such perturbations are derived, generalizing previous work initiated by M. Gleiser, and shown to give rise to a two-channel Schrödinger operator. Using standard tools from the literature, we show that for each fixed value $\ell$ of the angular momentum number, there exists a family of $\ell$-boson stars which are linearly stable with respect to radial fluctuations; in this case the perturbations oscillate in time with given characteristic frequencies which are computed and compared with the results from a nonlinear numerical simulation. Further, there is also a family of $\ell$-boson stars which are linearly unstable. The two families are separated by the configuration with maximum mass. These results are qualitatively similar to the corresponding stability results of the standard boson stars with $\ell=0$, and they imply the existence of new stable configurations that are more massive and compact than usual boson stars.

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arXiv2021

Rotating Boson Stars Using Finite Differences and Global Newton Methods

We study Rotating Boson Star initial data for Numerical Relativity as previously considered by Yoshida and Eriguchi, Lai (arXiv:gr-qc/0410040v2), and Grandclement, Somé and Gourgoulhon (arXiv:1405.4837v3). We use a 3 + 1 decomposition as presented by Gourgoulhon (arXiv:1003.5015v2) and Alcubierre, adapted to an axisymmetric quasi-isotropic spacetime with added regularization at the axis following work by Ruíz, Alcubierre and Núñez (arXiv:0706.0923v2) and Torres. The Einstein-Klein-Gordon equations result in a system of six-coupled, elliptic, nonlinear equations with an added unknown for the scalar field's frequency $ω$. Utilizing a Cartesian two-dimensional grid, finite differences, Global Newton Methods adapted from Deuflhard, the sparse direct linear solver PARDISO, and properly constraining all variables generates data sets for rotation azimuthal integers $l \in [0, 6]$. Our numerical implementation, published in GitHub, is shown to correctly converge both with respect to the resolution size and boundary extension (fourth-order and third-order, respectively). Thus, global parameters such as the Komar masses and angular momenta can be precisely calculated to characterize these spacetimes. Furthermore, analyzing the full family at fixed rotation integer produces maximum masses and minimum frequencies. These coincide with previous results in literature for $l \in [0,2]$ and are new for $l > 2$. In particular, the study of high-amplitude and localized scalar fields in axial symmetry is revealed to be only possible by adding the sixth regularization variable.

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