arXiv subjects

Alberto Diez-Tejedor

Publications and source records attributed to Alberto Diez-Tejedor.

At least 19 recordsLinked to original sources

arXiv2026

The continuum spectrum of nonrelativistic multi-frequency Proca stars

Multi-frequency Proca stars are excited selfgravitating solutions of the $s=1$ Schrödinger-Poisson system that generalize the conventional stationary states of a massive vector field. Unlike stationary states, which are characterized by a single oscillation frequency, multi-frequency configurations exhibit a quasi-periodic dynamics involving two or three distinct frequencies. In this paper, we present a systematic study of the spectrum of spherical multi-frequency Proca stars and show that, at fixed particle number, they form continuous families interpolating between discrete stationary states of constant linear polarization. Furthermore, we analyze their stability and demonstrate that a subset of these multi-frequency configurations are linearly stable against general perturbations. In particular, we show that a necessary, although not sufficient, condition for stability is the presence of a non-negligible nodeless component, and that radial stability alone is not sufficient to guarantee full linear stability. Finally, we briefly discuss the potential implications of multi-frequency states for proving the particle spin in ultralight dark matter models.

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

Linear stability of nonrelativistic Proca stars

We study the linear stability of nonrelativistic Proca stars under generic perturbations. Using a combination of analytic and numerical methods, we demonstrate that, as expected, the ground state is always mode-stable. Additionally, we identify several mode-stable spherically symmetric excited states, including stationary states of constant and radial polarization, as well as multi-frequency states in case that the spin-spin selfinteraction vanishes. The existence of stable excited states may have implications for spin-$1$ ultralight dark matter models.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

arXiv2025

Nonrelativistic Proca stars: Spherical stationary and multi-frequency states

In this paper we follow an effective theory approach to study the nonrelativistic limit of a selfgravitating and selfinteracting massive vector field. Our effective theory is characterized by three parameters: the field's mass $m_0$ and the selfinteraction constants $λ_n$ and $λ_s$. For definiteness, we focus on a systematic study of the equilibrium configurations, commonly referred to as Proca stars when they have finite energy. We identify two different types of Proca stars, depending on the specific sector of the effective theory that we are exploring. In the generic sector, defined by $λ_s\neq 0$, all equilibrium configurations are stationary states described by wave functions that evolve harmonically in time. However, in the symmetry-enhanced sector, for which $λ_s=0$, there exist multi-frequency states whose wave functions oscillate with two or three distinct frequencies in addition to the stationary states. We determine the conditions under which a ground state configuration with fixed particle number exists. When these conditions are met, we prove that the lowest energy is reached by a stationary spherically symmetric configuration of constant polarization that is linear or circular depending on the sign of $λ_s$. We numerically construct some illustrative examples of spherical stationary and multi-frequency solutions, analyze their properties, and compare them with our analytical predictions. Unlike stationary states and other soliton configurations, which form a discrete set in the solution space associated with fixed particle number, the symmetry-enhanced sector exhibits a continuum of solutions with multi-frequency states connecting stationary states of constant polarization.

gr-qc↗

arXiv2024

On the linear stability of nonrelativistic selfinteracting boson stars

In this paper we study the linear stability of selfinteracting boson stars in the nonrelativistic limit of the Einstein-Klein-Gordon theory. For this purpose, based on a combination of analytic and numerical methods, we determine the behavior of general linear perturbations around the stationary and spherically symmetric solutions of the Gross-Pitaevskii-Poisson system. In particular, we conclude that ground state configurations are linearly stable if the selfinteraction is repulsive, whereas there exist a state of maximum mass that divides the stable and the unstable branches in case the selfinteraction is attractive. Regarding the excited states, they are in general unstable under generic perturbations, although we identify a stability band in the first excited states of the repulsive theory. This result is independent of the mass of the scalar field and the details of the selfinteraction potential, and it is in contrast to the situation of vanishing selfinteraction, in which excited states are always unstable.

gr-qc↗

arXiv2023

Cosmic Energy Density: Particles, Fields and the Vacuum

We revisit the cosmic evolution of the energy density of a quantized free scalar field and assess under what conditions the particle production and classical field approximations reproduce its correct value. Because the unrenormalized energy-momentum tensor diverges in the ultraviolet, it is necessary to frame our discussion within an appropriate regularization and renormalization scheme. Pauli-Villars avoids some of the drawbacks of adiabatic subtraction and dimensional regularization and is particularly convenient in this context. In some cases, we can predict the evolution of the energy density irrespectively of the quantum state of the field modes. To further illustrate our results we focus however on the {\it in} vacuum, the preferred quantum state singled out by inflation, and explore to what extent the latter determines the subsequent evolution of the energy density regardless of the unknown details of reheating. We contrast this discussion with examples of transitions to radiation domination that avoid some of the problems of the one commonly studied in the literature, and point out some instances in which the particle production or the classical field approximations lead to the incorrect energy density. Along the way, we also elaborate on the connection of our analysis to dynamical dark energy models and axion-like dark matter candidates.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

arXiv2021

Horndeski stars

We establish the existence of time-dependent solitons in a modified gravity framework, which is defined by the low energy limit of theories with a weakly broken galileon symmetry and a mass term. These are regular vacuum configurations of finite energy characterized by a single continuous parameter representing the amplitude of the scalar degree of freedom at the origin. When the central field amplitude is small the objects are indistinguishable from boson stars. In contrast, increasing the central value of the amplitude triggers the effect of higher derivative operators in the effective theory, leading to departures from the previous solutions, until the theory becomes strongly coupled and model-dependent. The higher order operators are part of the (beyond) Horndeski theory, hence the name of the compact objects. Moreover, a remnant of the galileon non-renormalization theorem guarantees that the existence and properties of these solutions are not affected by quantum corrections. Finally, we discuss the linear stability under small radial perturbations, the mass-radius relation, the compactness, the appearance of innermost stable circular orbits and photon spheres, and some astrophysical signatures (accretion disks, gravitational radiation and lensing) that may be relevant to falsify the model.

gr-qc↗

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.

gr-qc↗

arXiv2019

Dynamical evolutions of $\ell$-boson stars in spherical symmetry

In previous work, we have found new static, spherically symmetric boson star solutions which generalize the standard boson stars by allowing a particular superposition of scalar fields in which each of the fields is characterized by a fixed value of its non-vanishing angular momentum number $\ell$. We call such solutions "$\ell$-boson stars". Here, we perform a series of fully non-linear dynamical simulations of perturbed $\ell$-boson stars in order to study their stability, and the final fate of unstable configurations. We show that for each value of $\ell$, the configuration of maximum mass separates the parameter space into stable and unstable regions. Stable configurations, when perturbed, oscillate around the unperturbed solution and very slowly return to a stationary configuration. Unstable configurations, in contrast, can have three different final states: collapse to a black hole, migration to the stable branch, or explosion (dissipation) to infinity. Just as it happens with $\ell=0$ boson stars, migration to the stable branch or dissipation to infinity depends on the sign of the total binding energy of the star: bound unstable stars collapse to black holes or migrate to the stable branch, whereas unbound unstable stars either collapse to a black hole or explode to infinity. Thus, the parameter $\ell$ allows us to construct a new set of stable configurations. All our simulations are performed in spherical symmetry, leaving a more detailed stability analysis including non-spherical perturbations for future work.

gr-qc↗

arXiv2018

$\ell$-Boson stars

We present new, fully nonlinear numerical solutions to the static, spherically symmetric Einstein-Klein-Gordon system for a collection of an arbitrary odd number $N$ of complex scalar fields with an internal $U(N)$ symmetry and no self-interactions. These solutions, which we dub $\ell$-boson stars, are parametrized by an angular momentum number $\ell=(N-1)/2$, an excitation number $n$, and a continuous parameter representing the amplitude of the fields. They are regular at every point and possess a finite total mass. For $\ell = 0$ the standard spherically symmetric boson stars are recovered. We determine their generalizations for $\ell > 0$, and show that they give rise to a large class of new static configurations which might have a much larger compactness ratio than $\ell=0$ stars.

gr-qc↗

arXiv2018

Horndeski dark matter and beyond

Starting from the Gleyzes-Langlois-Piazza-Vernizzi action, we derive the most general effective theory that is invariant under internal shifts and a $\mathbb{Z}_2$ mirror symmetry in the scalar sector. Contrary to what one may think, this model presents a dark matter tracker previous to the dark energy domination. We show that, in an empty universe and to linear order in perturbations, the scalar mode clusters in exactly the same way as standard nonrelativistic cold dark matter. This also holds for the subsector of the theory where the speed of propagation of gravitational waves equals that of light, in agreement with the recent multimessenger observation. However, the inclusion of standard model particles introduces nontrivial couplings of the gravitational scalar mode to baryons, modifying their clustering properties. We argue that no arrangement of the parameters of the model can reduce the extra scalar to precisely behave as cold dark matter.

gr-qc↗

arXiv2018

Verlinde's emergent gravity versus MOND and the case of dwarf spheroidals

In a recent paper, Erik Verlinde has developed the interesting possibility that spacetime and gravity may emerge from the entangled structure of an underlying microscopic theory. In this picture, dark matter arises as a response to the standard model of particle physics from the delocalized degrees of freedom that build up the dark energy component of the Universe. Dark matter physics is then regulated by a characteristic acceleration scale $a_0$, identified with the radius of the (quasi)-de Sitter universe we inhabit. For a point particle matter source, or outside an extended spherically symmetric object, MOND's empirical fitting formula is recovered. However, Verlinde's theory critically departs from MOND when considering the inner structure of galaxies, differing by a factor of 2 at the centre of a regular massive body. For illustration, we use the eight classical dwarf spheroidal satellites of the Milky Way. These objects are perfect testbeds for the model given their approximate spherical symmetry, measured kinematics, and identified missing mass. We show that, without the assumption of a maximal deformation, Verlinde's theory can fit the velocity dispersion profile in dwarf spheroidals with no further need of an extra dark particle component. If a maximal deformation is considered, the theory leads to mass-to-light ratios that are marginally larger than expected from stellar population and formation history studies. We also compare our results with the recent phenomenological interpolating MOND function of McGaugh {\it et al}, and find a departure that, for these galaxies, is consistent with the scatter in current observations.

astro-ph.CO↗

arXiv2017

Self-gravitating black hole scalar wigs

It has long been known that no static, spherically symmetric, asymptotically flat Klein-Gordon scalar field configuration surrounding a nonrotating black hole can exist in general relativity. In a series of previous papers we proved that, at the effective level, this no-hair theorem can be circumvented by relaxing the staticity assumption: for appropriate model parameters there are quasi-bound scalar field configurations living on a fixed Schwarzschild background which, although not being strictly static, have a larger lifetime than the age of the universe. This situation arises when the mass of the scalar field distribution is much smaller than the black hole mass, and following the analogies with the hair in the literature we dubbed these long-lived field configurations wigs. Here we extend our previous work to include the gravitational backreaction produced by the scalar wigs. We derive new approximate solutions of the spherically symmetric Einstein-Klein-Gordon system which represent self-gravitating scalar wigs surrounding black holes. These configurations interpolate between boson star configurations and Schwarzschild black holes dressed with the long-lived scalar test field distributions discussed in previous papers. Nonlinear numerical evolutions of initial data sets extracted from our approximate solutions support the validity of our approach. Arbitrarily large lifetimes are still possible, although for the parameter space that we analyze in this paper they seem to decay faster than the quasi-bound states. Finally, we speculate about the possibility that these configurations could describe the innermost regions of dark matter halos.

gr-qc↗

arXiv2017

Cosmological production of ultralight dark matter axions

The highly populated, low-energy excitations of a scalar field of mass $m_a\sim 10^{-22}\,\textrm{eV}$ can represent the full dark matter content of the universe and alleviate some tensions in the standard cosmological scenario on small-scales. This {\it fuzzy dark matter} component is commonly assumed to arise as the consequence of a new axion-like particle in the matter sector, yet for simplicity it is usually modeled in terms of a simple free quadratic field. In this paper we consider how the cosmological constraints are modified when the effects of an instanton potential and temperature-dependent mass are included. Current isocurvature and tensor bounds confirms that this particle should be formed before the end of a low-scale inflation period with Hubble parameter $H_I\lesssim 2.5\times 10^{12}\,\textrm{GeV}$, in accordance with previous free-field analysis. The axion decay constant, $f_a$, which fixes axion couplings, appears in the instanton potential and determines the relic abundance, the stability of galaxy cores to axion emission, and the direct searches of fuzzy dark matter. If the axion mass is $T$-independent, we find that $f_a\gtrsim 10^{16}\,\text{GeV}$ is required in order to reach the observed relic density without fine tuning the initial conditions, while for a $T$-dependent case this bound can be lowered by an order of magnitude. However, the anharmonicities in the instanton potential, and mainly a $T$-dependent mass, can delay the onset of field oscillations, leading to larger physical suppression scales in the matter power spectrum for a fixed zero-temperature axion mass. This may favor a string or accidental axion over one emerging from a strongly coupled gauge sector if this model is required to provide large galactic halo cores while simultaneously satisfying observational constraints from cosmic structure formation.

hep-ph↗