Scalar Field Configurations Research Articles

Equilibrium spherical shell of condensed matter around a scalar naked singularity

From a observational point of view, the central regions of scalar naked singularities possess a very special spacetime geometry, which in turn leads to existence of unusual orbital motion near the centers. We consider naked singularities in the model of static, spherically symmetric, asymptotically flat configurations of a self-gravitating scalar field minimally coupled to gravity. In this case, the effective potential of test particles orbiting around a scalar naked singularity has a minimum even at zero specific angular momentum. This means that the baryonic matter, captured by the naked singularity in the region of gravitational potential well near the center, will eventually be concentrated in some spherical shell, which will be in hydrostatic equilibrium after cooling. We find the conditions of hydrostatic equilibrium of the shell for the polytropic equation of state. In order to show the observational consequences of the possible existence of such configurations as real astrophysical objects, in particular in relation to tidal disruption events, we consider a simple illustrative example.

Self-interacting gravitational atoms in the strong-gravity regime

We numerically investigate free and self-interacting ultralight scalar fields around black holes in General Relativity. We focus on complex scalar fields Φ whose self-interactions are described by the quartic potential V ∝ λ |Φ|4, and ignore the black hole spin in order to disentangle the effects of self interactions on the boson cloud. Using the spectral solver Kadath, we compute quasi-equilibrium configurations of the dominant eigenstates, including their backreaction on the spacetime metric. For scenarios with -10-2 ≲ λ ≲ 10-2 we find the mass of the self-interacting scalar cloud to be up to ∼ 70% larger than that of a free scalar cloud, though the additional backreaction effect on the spacetime metric is only up to ∼ 1% due to the low-density nature of the bosonic configurations. In this region of parameter space we observe approximate quadratic scalings between the mass of the cloud with λ, the scalar field amplitude, and the couplings between these two parameters. For systems with λ beyond this range, the eigenfrequencies differ sufficiently from the known free-test-field values used as inputs in our numerical setupto make the results, though convergent, physically unreliable.This bounds the range of λ in which the free scalar field solution remains a good approximation to self-interacting scalar field configurations. Our work is among the first nonperturbative explorations of self-interacting bosonic clouds around black holes, yielding detailed new insights into such systems in the nonlinear regime, while also overcoming technical challenges and quantifying limitations. Additionally, our results provide useful inputsfor fully dynamical numerical relativity simulations and for future explorations of spinning black holes and real scalar fields.

Self-interacting scalar field distributions around Schwarzschild black holes

Long-lived configurations of massive scalar fields around black holes may form if the coupling between the mass of the scalar field and the mass of the black hole is very small. In this work we analyze the effect of self-interaction in the distribution of the long-lived cloud surrounding a static black hole. We consider both attractive and repulsive self-interactions. By solving numerically the Klein Gordon equation on a fixed background in the frequency domain, we find that the spatial distribution of quasi stationary states may be larger as compared to the non interacting case. We performed a time evolution to determine the effect of the self-interaction on the life time of the configurations our findings indicate that the contribution of the self-interaction is subdominant.

Analytical investigations on non-minimally coupled scalar fields outside neutral reflecting shells

We study the existence of scalar fields outside neutral reflecting shells. We consider static massive scalar fields non-minimally coupled to the Gauss–Bonnet invariant. We analytically investigated properties of scalar fields through the scalar field equation. In the small scalar field mass regime, we derive a compact resonance formula for the allowed masses of scalar fields in the composed scalar field and shell configurations.

On the stability of scale-invariant black holes

Quadratic scale-invariant gravity non minimally coupled to a scalar field provides a competitive model for inflation, characterized by the transition from an unstable to a stable fixed point, both characterized by constant scalar field configurations. We provide a complementary analysis of the same model in the static, spherically symmetric setting, obtaining two Schwarzschild-de Sitter solutions, which corresponds to the two fixed points existing in the cosmological scenario. The stability of such solutions is thoroughly investigated from two different perspectives. First, we study the system at the classical level by the analysis of linear perturbations. In particular, we provide both analytical and numerical results for the late-time behavior of the perturbations, proving the stable and unstable character of the two solutions. Then we perform a semi-classical, non-linear analysis based on the Euclidean path integral formulation. By studying the difference between the Euclidean on-shell actions evaluated on both solutions, we prove that the unstable one has a meta-stable character and is spontaneously decaying into the stable fixed point which is always favoured.

ZN -balls: Solitons from ZN -symmetric scalar field theory

We discuss the conditions under which static, finite-energy, configurations of a complex scalar field $\phi$ with constant phase and spherically symmetric norm exist in a potential of the form $V(\phi^*\phi, \phi^N+\phi^{*N})$ with $N\in\mathbb{N}$ and $N\geq2$, i.e. a potential with a $Z_N$-symmetry. Such configurations are called $Z_N$-balls. We build explicit solutions in $(3+1)$-dimensions from a model mimicking effective field theories based on the Polyakov loop in finite-temperature SU($N$) Yang-Mills theory. We find $Z_N$-balls for $N=$3, 4, 6, 8, 10 and show that only static solutions with zero radial node exist for $N$ odd, while solutions with radial nodes may exist for $N$ even.

Dynamics of a nonminimally coupled scalar field in asymptotically AdS 4 spacetime

We numerically investigate the stability of four-dimensional asymptotically anti-de Sitter (AdS 4) spacetime for a class of nonminimally coupled scalar field theories. In particular, we study how the coupling affects the formation of black holes, and the transfer of energy to different spatial/temporal scales. We conclude by detailing the well-known analogy between the nonminimally coupled scalar-field stress-energy tensor and that of a viscous relativistic fluid, and discuss the limitations of that analogy when it is applied to anisotropic scalar field configurations in asymptotically AdS spacetimes.

Slowly rotating spacetimes with scalar hair

We consider asymptotically flat, rotating configurations of a selfgravitating real scalar field minimally coupled to Einstein gravity. For the sake of completeness and to introduce convenient notation, we formulate the EinsteinKlein-Gordon equations in the orthonormal tetrad uniquely associated with the metric of a nonstationary axisymmetric spacetime. First, in the stationary case, we study Bianchi identities to find appropriate variants for reducing the EinsteinKlein-Gordon system to a complete subsystem of independent equations. It turns out that this procedure can be performed in three ways. Second, assuming that the rotation is slow, the full system of these equations is linearized about a spherically symmetric scalar field configuration, which may be thought of as some exact solution. In doing so, we do not assume that the scalar field is small, and do not specify the type of the basic spherically symmetric configuration, which can be a black hole, a naked singularity, or a wormhole.

Spin-charge induced scalarization of Kerr-Newman black-hole spacetimes

It has recently been demonstrated that Reissner-Nordström black holes in composed Einstein-Maxwell-scalar field theories can support static scalar field configurations with a non-minimal negative coupling to the Maxwell electromagnetic invariant of the charged spacetime. We here reveal the physically interesting fact that scalar field configurations with a non-minimal positive coupling to the spatially-dependent Maxwell electromagnetic invariant mathcal{F} ≡ FμνFμν can also be supported in black-hole spacetimes. Intriguingly, it is explicitly proved that the positive-coupling black-hole spontaneous scalarization phenomenon is induced by a non-zero combination a ∙ Q ≠ 0 of both the spin a ≡ J/M and the electric charge Q of the central supporting black hole. Using analytical techniques we prove that the regime of existence of the positive-coupling spontaneous scalarization phenomenon of Kerr-Newman black holes with horizon radius r+(M, a, Q) and a non-zero electric charge Q (which, in principle, may be arbitrarily small) is determined by the critical onset line (a/r+)critical = sqrt{2} − 1. In particular, spinning and charged Kerr-Newman black holes in the composed Einstein-Maxwell-scalar field theory are spontaneously scalarized by the positively coupled fields in the dimensionless charge regime 0<frac{Q}{M}le sqrt{2sqrt{2}-2} if their dimensionless spin parameters lie above the critical onset line frac{a(Q)}{M}ge {left[frac{a(Q)}{M}right]}_{mathrm{critical}}=frac{1+sqrt{1-2left(2-sqrt{2}right){left(Q/Mright)}^2}}{2sqrt{2}} .

Dark Range of ω In Brans-Dicke Gravity

The variational field equations of Brans-Dicke scalar-tensor theory of gravitation that is coupled to a mass-varying sterile neutrino field are presented in Riemannian and non-Riemannian setting in the language of exterior differential forms over four-dimensional spacetime. In a gravitational plane wave geometry in Rosen coordinates, with the scalar field set equal to a constant, the field equations admit ghost neutrino solutions. These correspond to Majorana spinor configurations for which the total neutrino stress-energy-momentum tensor vanishes. We show here that in the absence of a sterile neutrino in the gravitational wave geometry, there are scalar field configurations for which the total scalar field stress-energy-momentum tensor vanishes for negative values of the Brans-Dicke parameter —3/2 < ω < 0.

Non-minimally coupled massive scalar field configurations supported by charged reflecting shells: Analytic treatment in the weak coupling regime

The physical and mathematical properties of bound-state matter configurations which are made of massive scalar fields with a non-trivial (non-minimal) coupling to the electromagnetic field of a central charged reflecting shell of radius Rs are studied analytically. In particular, we explicitly prove that the Klein-Gordon wave equation for the composed charged-reflecting-shell-nonminimally-coupled-linearized-massive-scalar-field system is amenable to an analytical treatment in the dimensionless weak coupling regime (or equivalently, in the dimensionless small-mass regime) μαQ≪1 (here μ,Q, and α are respectively the proper mass of the non-minimally coupled scalar field, the electric charge of the spherically symmetric supporting shell, and the non-minimal coupling parameter of the composed Maxwell-scalar theory). We derive a remarkably compact resonance formula {μ(α,Q,Rs;n)}n=1n=∞ for the allowed masses of the supported spatially regular scalar fields in the composed charged-shell-nonminimally-coupled-massive-scalar-field bound-state configurations.

Ghost of vector fields in compact stars

Spontaneous scalarization is a mechanism that allows a scalar field to go undetected in weak gravity environments and yet develop a nontrivial configuration in strongly gravitating systems. At the perturbative level it manifests as a tachyonic instability around spacetimes that solve Einstein's equations. The endpoint of this instability is a nontrivial scalar field configuration that can significantly modify a compact object's structure and can produce observational signatures of the scalar field's presence. Does such a mechanism exists for vector fields? Here we revisit the model that constitutes the most straightforward generalization of the original scalarization model to a vector field and perform a perturbative analysis. We show that a ghost appears as soon as the square of the naive effective mass squared becomes negative anywhere. This result poses a serious obstacle in generalizing spontaneous scalarization to vector fields.

Planar black holes configurations and shear viscosity in arbitrary dimensions with shift and reflection symmetric scalar-tensor theories

In higher dimensions, we explore planar hairy black hole configurations for a special subclass of the Horndeski theory defined by two coupling functions depending on the kinetic term and enjoying shift symmetry and reflection symmetry. For this analysis, we derive a set of new solutions given by time-dependent as well as time-independent scalar field configurations. Additionally, we calculate their thermodynamic quantities by using Wald formalism satisfying the first law of thermodynamics as well as a Smarr relation. Together with the above, the Wald procedure allows us to compute the shear viscosity, showing that for a suitable choice of the coupling functions the Kovtun-Son-Starinets bound is violated.

Electroweak skyrmions in the HEFT

We study the existence of skyrmions in the presence of all the electroweak degrees of freedom, including a dynamical Higgs boson, with the electroweak symmetry being non-linearly realized in the scalar sector. For this, we use the formulation of the Higgs Effective Field Theory (HEFT). In contrast with the linear realization, a well-defined winding number exists in HEFT for all scalar field configurations. We classify the effective operators that can potentially stabilize the skyrmions and numerically find the region in parameter spaces that support them. We do so by minimizing the static energy functional using neural networks. This method allows us to obtain the minimal-energy path connecting the vacuum to the skyrmion configuration and calculate its mass and radius. Since skyrmions are not expected to be produced at colliders, we explore the experimental and theoretical bounds on the operators that generate them. Finally, we briefly consider the possibility of skyrmions being dark matter candidates.

Radially symmetric scalar solitons

A class of noncanonical effective potentials is introduced allowing stable, radially symmetric, solutions to first order Bogomol'nyi equations for a real scalar field in a fixed spacetime background. This class of effective potentials generalizes those found previously by Bazeia, Menezes, and Menezes [Phys.Rev.Lett. 91 (2003) 241601] for radially symmetric defects in a flat spacetime. Use is made of the "on-shell method" introduced by Atmaja and Ramadhan [Phys.Rev.D 90 (2014) 10, 105009] of reducing the second order equation of motion to a first order one, along with a constraint equation. This method and class of potentials admits radially symmetric, stable solutions for four dimensional static, radially symmetric spacetimes. Stability against radial fluctuations is established with a modified version of Derrick's theorem, along with demonstrating that the radial stress vanishes. Several examples of scalar field configurations are given.

Demonstration of minisuperspace quantum cosmology using quantum computational algorithms on IBM quantum computer

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum cosmology, we learn about the dynamics of the universe without constructing a complete theory of quantum gravity. Since the universal wavefunction exists in an infinite-dimensional superspace over all possible 3D metrics and modes of matter configurations, we take minisuperspaces for our work by constraining the degrees of freedom to particular 3D metrics and uniform scalar field configurations. Here, we consider a wide variety of cosmological models. We begin by analyzing an anisotropic universe with cosmological constant and classical radiation. We then study the results for higher derivatives, Kaluza–Klein theories and string dilaton in quantum cosmology. We use IBM’s Quantum Information Science Kit (QISKit) python library and the Variational Quantum Eigensolver (VQE) algorithm for studying these systems. The VQE algorithm is a hybrid algorithm that uses the variational approach and interleaves quantum and classical computations in order to find the minimum eigenvalue of the Hamiltonian for a given system. The minimum eigenvalue of the Hamiltonian obtained will serve as a boundary condition for the given wavefuntion.

Gravitational waves from dark sectors, oscillating inflatons, and mass boosted dark matter

Gravitational wave signatures from dynamical scalar field configurations provide a compelling observational window on the early universe. Here we identify intriguing connections between dark matter and scalars fields that emit gravitational waves, either through a first order phase transition or oscillating after inflation. To study gravitational waves from first order phase transitions, we investigate a simplified model consisting of a heavy scalar coupled to a vector and fermion field. We then compute gravitational wave spectra sourced by inflaton field configurations oscillating after E-Model and T-Model inflation. Some of these gravitational wave signatures can be uncovered by the future Big Bang Observatory, although in general we find that MHz-GHz frequency gravitational wave sensitivity will be critical for discovering the heaviest dark sectors. Intriguingly, we find that scalars undergoing phase transitions, along with E-Model and T-Model potentials, can impel a late-time dark matter mass boost and generate up to Planck mass dark matter. For phase transitions and oscillating inflatons, the largest dark matter mass boosts correspond to higher amplitude stochastic gravitational wave backgrounds.

Boson stars in f(T) extended theory of gravity

Spherically symmetric configurations of the non-interacting massive complex scalar field, representing non-rotating boson stars, are considered within the framework of the modified torsion based $f(T)$ gravity, with $f(T) = T + \alpha \, T^2/2$. We find that with sufficiently large negative value of $\alpha$ the mass of the boson stars can be made arbitrarily large. This is in contrast to General Relativity where an upper bound, $M_{max} \sim M_{Planck}^2/m$, to the mass of the boson stars built from the non-interacting scalar field exists and where the masses of boson stars in the astrophysical regime can be obtained only with the introduction of the scalar field self-interaction. With sufficiently large negative $\alpha$ we also find negative gravitational binding energy for all masses, which can be seen as an indication of the stability of such configurations. In its positive regime, $\alpha$ can not be made arbitrarily large as a phase transition in the stress--energy components of the $f(T)$-fluid develops. This phenomenon has already been reported to occur in polytropic stars constructed within the $f(T)$ gravity theory.

Exact solution of the 1D Dirac equation for the inverse-square-root potential 1/x$1/\sqrt{x}$

Abstract We present the exact solution of the 1D Dirac equation for the inverse-square-root potential 1 / x $1/\sqrt{x}$ for several configurations of vector, pseudo-scalar, and scalar fields. Each fundamental solution of the problem can be written as an irreducible linear combination of two Hermite functions of a scaled and shifted argument. We derive the exact equations for bound-state energy eigenvalues and construct accurate approximations for the energy spectrum.

Reissner-Nordström black holes supporting nonminimally coupled massive scalar field configurations

It has recently been demonstrated that static spatially regular scalar fields, which are non-minimally coupled to the electromagnetic field of a charged central black hole, can be supported in the exterior regions of the black-hole spacetime. In the present paper we use {\it analytical} techniques in order to study the physical and mathematical properties of the externally supported linearized scalar field configurations (scalar 'clouds') in the dimensionless large-mass regime $\mu r_+\gg1$ (here $\mu$ and $r_+$ are respectively the proper mass of the supported scalar field and the outer horizon radius of the central supporting black hole). In particular, we derive a remarkably compact analytical formula for the discrete resonant spectrum $\{\alpha_n(\mu;Q/M)\}_{n=0}^{n=\infty}$ which characterizes the dimensionless coupling parameter of the composed black-hole-non-minimally-coupled-linearized-massive-scalar-field configurations. The physical significance of this resonant spectrum stems from the fact that, for a given value of the dimensionless black-hole electric charge $Q/M$, the fundamental (smallest) eigenvalue $\alpha_0(\mu)$ determines the critical existence-line of the composed black-hole-massive-field system, a boundary line which separates non-linearly coupled hairy charged-black-hole-massive-scalar-field configurations from bald Reissner-Nordstr\"om black holes. The analytical results derived in this paper are confirmed by direct numerical computations.