Scalar Field Configurations Research Articles

Charged reflecting shells supporting non-minimally coupled massless scalar field configurations

We study analytically the physical and mathematical properties of spatially regular massless scalar field configurations which are non-minimally coupled to the electromagnetic field of a spherically symmetric charged reflecting shell. In particular, the Klein–Gordon wave equation for the composed charged-reflecting-shell-nonminimally-coupled-linearized-massless-scalar-field system is solved analytically. Interestingly, we explicitly prove that the discrete resonance spectrum {R_{text {s}}(Q,alpha ,l;n)}^{n=infty }_{n=1} of charged shell radii that can support the non-minimally coupled massless scalar fields can be expressed in a remarkably compact form in terms of the characteristic zeros of the Bessel function (here Q, alpha , and l are respectively the electric charge of the central supporting shell, the dimensionless non-minimal coupling parameter of the Maxwell-scalar theory, and the angular harmonic index of the supported scalar configuration).

Large-misalignment mechanism for the formation of compact axion structures: Signatures from the QCD axion to fuzzy dark matter

Axions are some of the best motivated particles beyond the Standard Model. We show how the attractive self-interactions of dark matter (DM) axions over a broad range of masses, from $10^{-22}$ eV to $10^7$ GeV, can lead to nongravitational growth of density fluctuations and the formation of bound objects. This structure formation enhancement is driven by parametric resonance when the initial field misalignment is large, and it affects axion density perturbations on length scales of order the Hubble horizon when the axion field starts oscillating, deep inside the radiation-dominated era. This effect can turn an otherwise nearly scale-invariant spectrum of adiabatic perturbations into one that has a spike at the aforementioned scales, producing objects ranging from dense DM halos to scalar-field configurations such as solitons and oscillons. We call this class of cosmological scenarios for axion DM production "the large-misalignment mechanism." We explore observational consequences of this mechanism for axions with masses up to $10$ eV. For axions heavier than $10^{-5}$ eV, the compact axion halos are numerous enough to significantly impact Earth-bound direct detection experiments, yielding intermittent but coherent signals with repetition rates exceeding one per decade and crossing times less than a day. These episodic increases in the axion density and kinematic coherence suggest new approaches for axion DM searches, including for the QCD axion. Dense structures made up of axions from $10^{-22}$ eV to $10^{-5}$ eV are detectable through gravitational lensing searches, and their gravitational interactions can also perturb baryonic structures and alter star formation. At very high misalignment amplitudes, the axion field can undergo self-interaction-induced implosions long before matter-radiation equality, producing potentially-detectable low-frequency stochastic gravitational waves.

On the Possible Role of a Nonlinear Inflaton Scalar Field in the Formation of Astrophysical Objects

Within the framework of GRT we consider equilibrium configurations of a self-gravitating nonlinear scalar field of a type that in cosmology is one of the models of an inflaton field. We show that such configurations for a suitable choice of parameters of the system of a gravitational and a scalar field can form wormholes and cosmic strings with different values of the azimuthal angle defect.

Geodesic motion near self-gravitating scalar field configurations

We study the geodesics motion of neutral test particles in the static spherically symmetric spacetimes of black holes and naked singularities supported by a selfgravitating real scalar field. The scalar field is supposed to model dark matter surrounding some strongly gravitating object such as the centre of our Galaxy. The behaviour of timelike and null geodesics very close to the centre of such a configuration crucially depends on the type of spacetime. It turns out that a scalar field black hole, analogously to a Schwarzschild black hole, has the innermost stable circular orbit and the (unstable) photon sphere, but their radii are always less than the corresponding ones for the Schwarzschild black hole of the same mass; moreover, these radii can be arbitrarily small. In contrast, a scalar field naked singularity has neither the innermost stable circular orbit nor the photon sphere. Instead, such a configuration has a spherical shell of test particles surrounding its origin and remaining in quasistatic equilibrium all the time. We also show that the characteristic properties of null geodesics near the centres of a scalar field naked singularity and a scalar field black hole of the same mass are qualitatively different.

Geodesic motion near self-gravitating scalar field configurations

We study the geodesics motion of neutral test particles in the static spherically symmetric spacetimes of black holes and naked singularities supported by a selfgravitating real scalar field. The scalar field is supposed to model dark matter surrounding some strongly gravitating object such as the centre of our Galaxy. The behaviour of timelike and null geodesics very close to the centre of such a configuration crucially depends on the type of spacetime. It turns out that a scalar field black hole, analogously to a Schwarzschild black hole, has the innermost stable circular orbit and the (unstable) photon sphere, but their radii are always less than the corresponding ones for the Schwarzschild black hole of the same mass; moreover, these radii can be arbitrarily small. In contrast, a scalar field naked singularity has neither the innermost stable circular orbit nor the photon sphere. Instead, such a configuration has a spherical shell of test particles surrounding its origin and remaining in quasistatic equilibrium all the time. We also show that the characteristic properties of null geodesics near the centres of a scalar field naked singularity and a scalar field black hole of the same mass are qualitatively different.

Geodesic motion near self-gravitating scalar field configurations

We study the geodesics motion of neutral test particles in the static spherically symmetric spacetimes of black holes and naked singularities supported by a selfgravitating real scalar field. The scalar field is supposed to model dark matter surrounding some strongly gravitating object such as the centre of our Galaxy. The behaviour of timelike and null geodesics very close to the centre of such a configuration crucially depends on the type of spacetime. It turns out that a scalar field black hole, analogously to a Schwarzschild black hole, has the innermost stable circular orbit and the (unstable) photon sphere, but their radii are always less than the corresponding ones for the Schwarzschild black hole of the same mass; moreover, these radii can be arbitrarily small. In contrast, a scalar field naked singularity has neither the innermost stable circular orbit nor the photon sphere. Instead, such a configuration has a spherical shell of test particles surrounding its origin and remaining in quasistatic equilibrium all the time. We also show that the characteristic properties of null geodesics near the centres of a scalar field naked singularity and a scalar field black hole of the same mass are qualitatively different.

Towards a viable effective field theory of mimetic gravity

We discuss mimetic gravity theories with direct couplings between the curvature and higher derivatives of the scalar field, up to the quintic order, which were proposed to solve the instability problem for linear perturbations around the FLRW background for this kind of models. Restricting to homogeneous scalar field configurations in the action, we derive degeneracy conditions to obtain an effective field theory with three degrees of freedom. However, performing the Hamiltonian analysis for a generic scalar field we show that there are in general four or more degrees of freedom. The discrepancy is resolved because, for a homogeneous scalar field profile, ∂iφ≈ 0, the Dirac matrix becomes singular, resulting in further constraints, which reduces the number of degrees of freedom to three. Similarly, in linear perturbation theory the additional scalar degree of freedom can only be seen by considering a non-homogeneous background profile of the scalar field. Therefore, restricting to homogeneous scalar fields these kinds of models provide viable explicitly Lorentz violating effective field theories of mimetic gravity.

Nonstationary self-gravitating configurations of scalar and electromagnetic fields

Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or stationary configurations. This is due to the objective complexity of solving the Einstein equations under the assumption of nonstationarity. We present an approach to constructing nonstationary configurations of a spherically symmetric nonlinear real scalar field and the electromagnetic field, which are assumed both to be minimally coupled to gravity. It is based on the isolation of one invariant equation written in terms of the characteristic function and scalar field potential. Using the proposed method, an exact nonstationary solution with a nontrivial topology of space-time will be constructed.

Gauss\u2013Bonnet black holes supporting massive scalar field configurations: the large-mass regime

It has recently been demonstrated that black holes with spatially regular horizons can support external scalar fields (scalar hairy configurations) which are non-minimally coupled to the Gauss–Bonnet invariant of the curved spacetime. The composed black-hole-scalar-field system is characterized by a critical existence line alpha =alpha (mu r_{text {H}}) which, for a given mass of the supported scalar field, marks the threshold for the onset of the spontaneous scalarization phenomenon [here {alpha ,mu ,r_{text {H}}} are respectively the dimensionless non-minimal coupling parameter of the field theory, the proper mass of the scalar field, and the horizon radius of the central supporting black hole]. In the present paper we use analytical techniques in order to explore the physical and mathematical properties of the marginally-stable composed black-hole-linearized-scalar-field configurations in the eikonal regime mu r_{text {H}}gg 1 of large field masses. In particular, we derive a remarkably compact analytical formula for the critical existence-line alpha =alpha (mu r_{text {H}}) of the system which separates bare Schwarzschild black-hole spacetimes from composed hairy (scalarized) black-hole-field configurations.

Spontaneous scalarization of charged Reissner-Nordström black holes: Analytic treatment along the existence line

It has recently been demonstrated that charged black holes can support spatially regular matter configurations made of massless scalar fields which are non-minimally coupled to the electromagnetic field of the charged spacetime. Intriguingly, using numerical techniques, it has been revealed that the resonant spectra of the composed charged-black-hole-nonminimally-coupled-scalar-field configurations are characterized by charge-dependent discrete scalarization bands α∈{[αn−(Q¯),αn+(Q¯]}n=0n=∞, where α is the dimensionless coupling constant of the theory and Q¯≡Q/M is the dimensionless charge-to-mass ratio of the central supporting black hole. In the present paper we use analytical techniques in order to study the physical and mathematical properties of the spatially regular non-minimally coupled scalar field configurations (linearized scalar clouds) which are supported by the central charged Reissner-Nordström black holes. In particular, we derive a remarkably compact formula for the discrete resonant spectrum {αn−(Q¯)}n=0n=∞ which characterizes the composed black-hole-linearized-field configurations along the existence-line of the system, the critical line which separates bare Reissner-Nordström black holes from hairy scalarized black-hole configurations. The analytical results are confirmed by direct numerical computations.

On instabilities of stationary scalar field configurations supported by reflecting compact stars

We study instabilities of the system composed of stationary scalar fields and asymptotically flat horizonless reflecting compact stars. In the probe limit, we obtain bounds on the scalar field frequency. Below this bound, stationary hairy stars are expected to suffer from nonlinear instabilities under massless field perturbations. In other words, we prove that stationary scalar hairy stars are unstable for scalar fields with small frequency.

Bound orbits near scalar field naked singularities

We study bound orbits near the centres of static, spherically symmetric, asymptotically flat configurations of a self-gravitating scalar field minimally coupled to gravity. In our approach, a nonlinear scalar field is considered as an idealized model of dark matter, and the main examples that we have in mind are the centres of galaxies. We consider both scalar field black holes and scalar field naked singularities (SFNSs). It turns out that the shape and parameters of a bound orbit depend crucially on the type of configuration. The lapse metric function of a SFNS and, consequently, the effective potential of a massive test particle with zero angular momentum have a global minimum. A SFNS has a static degenerated orbit on which a test particle, having zero angular momentum and the minimum of its energy, remains at rest at all times. This implies that there exists a spherical shell consisting of cold gas or dust, which for a distant observer can look like the shadow of a black hole. We also study the shape of noncircular bound orbits close to the centres of SFNSs and show that their angles of precession are negative.

Classification of shift-symmetric Horndeski theories and hairy black holes

No-hair theorems for scalar-tensor theories imply that the trivial scalar field configuration is the unique configuration around stationary black hole spacetimes. The most basic assumption in these theorems is that a constant scalar configuration is actually admissible. In this paper, we classify shift-symmetric Horndeski theories according to whether or not they admit the trivial scalar configuration as a solution and under which conditions. Local Lorentz symmetry and the presence of a linear coupling between the scalar field and Gauss-Bonnet invariant plays feature prominently in this classification. We then use the classification to show that any theory without linear Gauss-Bonnet coupling that respects Local Lorentz symmetry admits all GR solutions. We also study the scalar hair configuration around black hole spacetimes in theories where the linear Gauss-Bonnet coupling is present. We show that the scalar hair of the configuration is secondary, fixed by the regularity of the horizon, and is determined by the black hole horizon properties.

Gravitational waves from bubble dynamics: beyond the envelope

We study gravitational-wave production from bubble dynamics (bubble collisions and sound waves) during a cosmic first-order phase transition with an analytic approach. We first propose modeling the system with the thin-wall approximation but without the envelope approximation often adopted in the literature, in order to take bubble propagation after collisions into account. The bubble walls in our setup are considered as modeling the scalar field configuration and/or the bulk motion of the fluid. We next write down analytic expressions for the gravitational-wave spectrum, and evaluate them with numerical methods. It is found that, in the long-lasting limit of the collided bubble walls, the spectrum grows from ∝ f3 to ∝ f1 in low frequencies, showing a significant enhancement compared to the one with the envelope approximation. It is also found that the spectrum saturates in the same limit, indicating a decrease in the correlation of the energy-momentum tensor at late times. We also discuss the implications of our results to gravitational-wave production both from bubble collisions (scalar dynamics) and sound waves (fluid dynamics).

Configurational entropy as a lifetime predictor and pattern discriminator for oscillons

Oscillons are long-lived, spherically-symmetric, attractor scalar field configurations that emerge as certain field configurations evolve in time. It has been known for many years that there is a direct correlation between the initial configuration's shape and the resulting oscillon lifetime: a shape memory. In this paper we use an information entropic measure known as differential configurational entropy (DCE) to obtain estimates of oscillon lifetimes in scalar field theories with symmetric and asymmetric double-well potentials. The time-dependent DCE is built form the Fourier-transform of the two-point correlation function of the energy density of the scalar field. We obtain a scaling law between oscillon lifetimes and measures obtained form the time varying DCE. We also show that DCE acts as a pattern discriminator, able to distinguish initial configurations that evolve into long-lived oscillons from other non-perturbative short-lived fluctuations.

Starobinsky inflation and dark energy and dark matter effects from quasicrystal like spacetime structures

The goal of this work on mathematical cosmology and geometric methods in modified gravity theories, MGTs, is to investigate Starobinsky-like inflation scenarios determined by gravitational and scalar field configurations mimicking quasicrystal, QC, like structures. Such spacetime aperiodic QCs are different from those discovered and studied in solid state physics but described by similar geometric methods. We prove that a inhomogeneous and locally anisotropic gravitational and matter field effective QC mixed continuous and discrete “ether” can be modelled by exact cosmological solutions in MGTs and Einstein gravity. The coefficients of corresponding generic off-diagonal metrics and generalized connections depend (in general) on all spacetime coordinates via generating and integration functions and, certain smooth and discrete parameters. Imposing additional nonholonomic constraints, prescribing symmetries for generating functions and solving the boundary conditions for integration functions and constants, we can model various nontrivial torsion QC structures or extract cosmological Levi-Civita configurations with diagonal metrics reproducing de Sitter (inflationary) like and other type homogeneous inflation and acceleration phases. Finally, we speculate how various dark energy and dark matter effects can be modelled by off-diagonal interactions and deformations of a nontrivial QC like gravitational vacuum structure and analogous scalar matter fields.

Scalar field configurations supported by charged compact reflecting stars in a curved spacetime

We study the system of static scalar fields coupled to charged compact reflecting stars through both analytical and numerical methods. We enclose the star in a box and our solutions are related to cases without box boundaries when putting the box far away from the star. We provide bottom and upper bounds for the radius of the scalar hairy compact reflecting star. We obtain numerical scalar hairy star solutions satisfying boundary conditions and find that the radius of the hairy star in a box is continuous in a range, which is very different from cases without box boundaries where the radius is discrete in the range. We also examine effects of the star charge and mass on the largest radius.

On the possibility that ultra-light boson haloes host and form supermassive black holes

Several observations suggest the existence of super-massive black holes (SMBH) at the centers of giant galaxies. However the mechanism under which these objects form remains non completely understood. In this work we review an alternative mechanism of formation of galactic SMBHs. This is, the collapse of ultra-light scalar field configurations playing the role of dark matter halos. Several works have studied this scenario and investigated its plausibility. The theory of collapse of scalar field configurations into compact objects has been extensively studied regarding to boson stars, in this work we extrapolate such results for models of galactic halos hosting central SMBHs. We construct the simplest setup of an ultra-light scalar field configuration laying in a Schwarzschild space-time for modeling a galactic system with a SMBH in the quasi-static limit. This model is applicable to systems either out of their accretion-phase at late times or either for those undergoing into a very slow accretion-phase, such as some early-type giant elliptic galaxies and bulges. On the other hand, very recent direct observation of Sagittarius A by the Event Horizon Telescope will open an era of explorations of the deep-inner galactic region of the Milky Way that will enable us to test and distinguish various dark matter models. Thus we use our model to give a very first step towards that direction. We derive the stellar kinematics induced by this sort dark matter to obtain information of the black hole's influence into the observable features of the velocity field of visible matter deep inside the galaxy. Thus we compute the radial velocity, acceleration and velocity dispersion densities for some realistic cases.

Charged reflecting stars supporting charged massive scalar field configurations

The recently published no-hair theorems of Hod, Bhattacharjee, and Sarkar have revealed the intriguing fact that horizonless compact reflecting stars cannot support spatially regular configurations made of scalar, vector and tensor fields. In the present paper we explicitly prove that the interesting no-hair behavior observed in these studies is not a generic feature of compact reflecting stars. In particular, we shall prove that charged reflecting stars can support charged massive scalar field configurations in their exterior spacetime regions. To this end, we solve analytically the characteristic Klein–Gordon wave equation for a linearized charged scalar field of mass mu , charge coupling constant q, and spherical harmonic index l in the background of a spherically symmetric compact reflecting star of mass M, electric charge Q, and radius R_{text {s}}gg M,Q. Interestingly, it is proved that the discrete set {R_{text {s}}(M,Q,mu ,q,l;n)}^{n=infty }_{n=1} of star radii that can support the charged massive scalar field configurations is determined by the characteristic zeroes of the confluent hypergeometric function. Following this simple observation, we derive a remarkably compact analytical formula for the discrete spectrum of star radii in the intermediate regime Mll R_{text {s}}ll 1/mu . The analytically derived resonance spectrum is confirmed by direct numerical computations.

On symmetry inheritance of nonminimally coupled scalar fields

We present the first symmetry inheritance analysis of fields non-minimally coupled to gravity. In this work we are focused on the real scalar field ϕ with nonminimal coupling of the form . Possible cases of symmetry noninheriting fields are constrained by the properties of the Ricci tensor and the scalar potential. Examples of such spacetimes can be found among those which are ‘dressed’ with the stealth scalar field, a nontrivial scalar field configuration with the vanishing energy–momentum tensor. We classify the scalar field potentials which allow symmetry noninheriting stealth field configurations on top of the exact solutions of the Einstein’s gravitational field equation with the cosmological constant.