Scalar Field Solutions Research Articles

Weak cosmic censorship with excited scalar fields and bound on charge-to-mass ratio

Recent study in [1] discovered that introducing a massive charged scalar field and requiring the Weak Gravity Conjecture (WGC) to hold can eliminate a class of Weak Cosmic Censorship Conjecture (WCCC) counterexamples in anti-de Sitter spacetime, indicating a potential connection between WCCC and WGC. In this paper, we extend the study to the case of excited-state scalar fields, and numerically construct the static solutions of excited massive charged scalar fields coupled to the Einstein-Maxwell field in four dimensional spacetime with asymptotically anti-de Sitter boundary conditions. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. However, after adding the scalar field with sufficiently large charge, the original counterexamples can be removed and cosmic censorship is preserved. We find this conclusion also applies to the excited-state of scalar field. There is a minimum value qcbound\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {q}_c^{\ extrm{bound}} $$\\end{document}. When the charge of the excited scalar field is larger than this minimum value, for sufficiently large boundary electric amplitude a, there will not appear a region with arbitrarily large curvature. That means there exists lower bound on the charge for excited state fields which protects cosmic censorship from being violated.

Scalar field solutions and energy bounds for modeling spatial oscillations in Schwarzschild black holes based on the Regge–Wheeler equation

This text discusses the behavior of solutions and the energy stability within Schwarzschild spacetimes, with a particular emphasis on the behavior of massless scalar fields under the influence of a non-rotating and spherically symmetric black hole. The stability of solutions in the proximity of the event horizon of black holes in general relativity remains an open question, especially given the difficulties introduced by minor perturbations that may resemble Kerr solutions. To address this, this work explores a simplified model, including massless scalar fields, to better understand perturbation behaviors around black holes under the Schwarzschild approach. We depart from Richard Price’s work in connection with how scalar, electromagnetic, and gravitational fields behave. The tortoise coordinate transformation is considered to set the stage for numerical solutions to the wave equations. Afterward, we explore energy estimates, which are used to gauge stability and wave behavior over time. Our analysis reveals that the time evolution of the energy does not exceed twice its initial value. Further and under the assumption of initial conditions in L2−spaces, we obtain an exponential decreasing behavior in the energy time evolution. A question to continue exploring is how perturbations in L2 in the initial conditions that introduce Kerr solutions as a second-order effect in the linearized equations perturb this obtained exponential decay.

Form Invariance of Raychaudhuri Equation in the Presence of Inflaton‐Type Fields

AbstractWe show that the Raychaudhuri equation (RE) remains form invariant for certain solutions of scalar fields whose Lagrangian is non‐canonical and of the form , with and the potential. Solutions exist for both homogeneous and inhomogeneous fields that are like inflatons. Certain recent observations indicate that the cosmos is inhomogeneous and thus their results are in sync with latest observations. So the RE can accommodate primordial inhomogeneities as well as cosmologically relevant scenarios.

Mass generation via nonlinear massive solution in Higgs potential and particle creations

The nonlinear massive plane wave solution of the classical scalar field in the Higgs potential is revisited to study the mass generation and particle creation. In particular, by assuming that the Higgs system is in the slightly excited state in early universe and it is described by the nonlinear solution, we study the mass generation mechanism for massive vector bosons and a heavy fermion in the quantum field theory around the nonlinear massive classical field. The nonlinear massive classical solution gives the transition from the vacuum to a pair of vector bosons and fermions. We present the new formulae of the probability density of the production process for particles in the standard model of elementary particle physics. The probability densities of the particle productions vanish when the nonlinear massive solution reduces to the constant solution (the classical vacuum expectation value); while the probability densities are expressed as the function of the free parameter in the classical solution in general case. We discuss the behavior of the probability densities for the three oscillating modes in the classical solution.

Accurate computation of the screening of scalar fifth forces in galaxies

Screening mechanisms allow light scalar fields to dynamically avoid the constraints that come from our lack of observation of a long-range fifth force. Galactic scale tests are of particular interest when the light scalar is introduced to explain the dark matter or dark energy that dominates our cosmology. To date, much of the literature that has studied screening in galaxies has described screening using simplifying approximations. In this work, we calculate numerical solutions for scalar fields with screening mechanisms in galactic contexts, and use these to derive new, precise conditions governing where fifth forces are screened. We show that the commonly used binary screened/unscreened threshold can predict a fifth force signal in situations where a fuller treatment does not, leading us to conclude that existing constraints might be overestimated.We show that various other approximations of the screening radius provide a more accurate proxy to screening, although they fail to exactly reproduce the true screening surface in certain regions of parameter space. As a demonstration of our scheme, we apply it to an idealised Milky Way and thus identify the region of parameter space in which the solar system is screened.

From Scalar Clouds to Rotating Hairy Black Holes

First, we review the solutions of a complex-valued scalar field, termed scalar clouds, with and without electric charge, when coupled to a rotating Kerr–Newman (electrically charged) or Kerr (neutral) black hole (BH), respectively. To this aim, we determine the conditions and parameters that characterize the existence of solutions that represent bound states, with an energy-momentum tensor that respect the symmetries of the underlying spacetimes, even if the backreaction of the field is not taken into account at this stage. In particular, we show that in the extremal Kerr scenario the cloud solutions exist only when the mass of the BH satisfies certain bounds, which are obtained by analyzing an effective potential associated with the radial dependency of the scalar clouds that leads to a Schrödinger-like equation. Second, when the backreaction of the field in the spacetime is taken into account, we present a family of stationary, axisymmetric and asymptotically flat solutions of the Einstein–Klein–Gordon system that represent genuine rotating hairy black holes (RHBHs) and provide different values of some global quantities associated with them, such as the Komar mass and the Komar angular momentum. We also compute RHBH solutions with nodes in the radial part of the scalar field and also for a higher azimuthal number m.

Study on Kalb–Ramond field localization in f(T) gravity theory with a noncanonical scalar field

In this paper, we investigate the localization of five-dimensional tensor gauge fields called Kalb–Ramond fields in the modified teleparallel braneworld models. The aforementioned branes are generated by gravity coupled to a real scalar field with nonstandard kinetic terms. For two specific forms of the noncanonical expressions, background scalar field solutions are particularly discussed in the presence of different forms of [Formula: see text] gravity. By applying nonminimal coupling functions in the tensor gauge field action, it is shown that massless zero modes of Kalb–Ramond gauge fields can be localized on the [Formula: see text] branes with noncanonical scalar fields. We also find that potentials of Kalb–Ramond massive modes are volcano-like regarding the equation of motion in the supersymmetric quantum mechanic scenario. Furthermore, the effects of parameters that control the deviation of the usual teleparallel theory are considered on the massless Kaluza–Klein mode and effective potential.

The phenomenology of quadratically coupled ultra light dark matter

We discuss models of ultralight scalar Dark Matter (DM) with linear and quadratic couplings to the Standard Model (SM). In addition to studying the phenomenology of linear and quadratic interactions separately, we examine their interplay. We review the different experiments that can probe such interactions and present the current and expected future bounds on the parameter space. In particular, we discuss the scalar field solution presented in [A. Hees, O. Minazzoli, E. Savalle, Y. V. Stadnik and P. Wolf, Phys.Rev.D 98 (2018) 6, 064051], and extend it to theories that capture both the linear and the quadratic couplings of the Dark Matter (DM) field to the Standard Model (SM). Furthermore, we discuss the theoretical aspects and the corresponding challenges for natural models in which the quadratic interactions are of phenomenological importance.

A new slow-rotating black hole solution in Chern-Simons axion of Einstein gravity

This research aims to incorporate an axionic field within the context of dynamical Chern-Simons (CS) gravity and investigate the behavior of a slowly rotating black hole (BH) within this theoretical framework. To the best of our knowledge, this is the first instance where such a problem has been tackled within the context of (CS) gravitational theory coupled with the axionic field. The Lagrangian of this theory includes two CS scalar field functions, denoted as ω(ϑ) and U(ϑ), where ϑ represents the CS scalar field. Our investigation involves calculating the equation related to the CS scalar field and demonstrating that deriving a solution necessitates imposing constraints on U and ω, specifically in the form of U′=ω, where U′≡dU(ϑ)dϑ. By utilizing the solution for the CS scalar field in other field equations, we reveal that the enigmatic function U can be expressed explicitly as U=ϑ2p+1, where p represents an integer with unrestricted values. In the instance where p=0, the CS Axion Einstein gravity theory [1] aligns with the study carried out in [2]. Furthermore, our analysis establishes that for positive values of p, the theory is capable of generating a significantly potent CS BH compared to the model derived in [2]. Moreover, our study delves into the geodesics of this BH, deriving its conserved quantities, orbital period, as well as its geodesic precession angle.

Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field

Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field

Conformally coupled scalar in Lovelock theory

In arbitrary higher dimension, we consider the combination of Lovelock gravity alongside a scalar-tensor action built out of higher order operators and Euler densities. The latter action is constructed in such a way as to ensure conformal invariance for the scalar field. For the combined version of these theories, we show the existence of black hole solutions interpreted as stealth configurations within Lovelock gravity theory. The scalar field solutions are endowed with an integration constant that may be identified as a scalar charge. In particular, we show that these stealth solutions can be extended to include a time-dependent scalar field despite the underlying theory being non shift symmetric. Finally, we present a procedure to obtain a nonconformally invariant action in even dimensions from the considered theory. For the target theory, the scalar field is not conformally coupled to gravity although the scalar field equation itself is conformally invariant. By means of this procedure, the black hole stealth configurations are converted into nonstealth black hole solutions, as discovered recently in four dimensions.

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.

Solitonic self-sustained charge and energy transport on the superconducting cylinder

We present an exact time-dependent solution for a charged scalar field on a two-dimensional cylinder, that can be interpreted as representing a long-standing excitation on a $S$-wave superconducting state, which propagates along a nanotube constructed out of twisted bilayer graphene. The solution has a topological charge characterized by an integer number, which counts the winding of the Higgs phase winds around the cylinder. The resulting electric current generates its own electromagnetic field in a self-consistent way, without the need of any external fields to keep it alive.

Localized scalar structures around static black holes

In this work we address a way to capture scalar field solutions on static spacetimes by using BPS formalism and relaxing the general covariance condition. We focus on configurations where the background geometry describes topological black holes and present both analytical and numerical solutions, in addition to discussing the use of conserved charges associated to such field configurations. The obtained solutions are radially stable and the zero-mode arising from the stability equation can be written analytically.

Erratum: Analytical scalar field solutions on Lifshitz spacetimes [Phys. Rev. D 105 , 016001 (2022)

In this work, we investigate the existence of analytic solutions of static scalar fields on Lifshitz spacetimes. We evade Derrick's theorem on curved spacetimes by breaking general covariance and use first-order formalism to obtain solutions with finite energy related to the time-translational invariance of the background geometry along with the energy-momentum tensor of the model. We show that such solutions exist and are stable in systems where the Lifshitz background geometry is fixed and the self-interaction potential of the scalar field explicitly depends on the radial coordinate present in the metric.

Exponentially generalized vortex

In this work, we propose an exponentially generalized Abelian model. We investigated the presence of vortex structures in models coupled to Maxwell and Chern-Simons fields. We chose to investigate the dynamics of the complex scalar field in models coupled separately to the Maxwell term and the Chern-Simons term. For this, we analyze the Bogomol'nyi equations in both cases to describe the static field configurations. An interesting result appears when we note that scalar field solutions generate degenerate minimum energy configurations by a factor of in Maxwell's case. On the other hand, in the Chern-Simons case, the solutions in this sector are degenerate by a factor of . Finally, we solve the Bogomol'nyi equations numerically and discuss our results.

How do spherical black holes grow monopole hair?

Black holes in certain modified gravity theories that contain a scalar field coupled to curvature invariants are known to possess (monopole) scalar hair while non-black-hole spacetimes (like neutron stars) do not. Therefore, as a neutron star collapses to a black hole, scalar hair must grow until it settles to the stationary black hole solution with (monopole) hair. In this paper, we study this process in detail and show that the growth of scalar hair is tied to the appearance and growth of the event horizon (before an apparent horizon forms), which forces scalar modes that would otherwise (in the future) become divergent to be radiated away. We prove this result rigorously in general first for a large class of modified theories, and then we exemplify the results by studying the temporal evolution of the scalar field in scalar Gauss-Bonnet gravity in two backgrounds: (i) a collapsing Oppenheimer-Snyder background, and (ii) a collapsing neutron star background. In case (i), we find an exact scalar field solution analytically, while in case (ii) we solve for the temporal evolution of the scalar field numerically, with both cases supporting the conclusion presented above. Our results suggest that the emission of a burst of scalar field radiation is a necessary condition for black hole formation in a large class of modified theories of gravity.

Curious case of the Buchdahl-Land-Sultana-Wyman-Ibañez-Sanz spacetime

We revisit Wyman's "other" scalar field solution of the Einstein equations and its Sultana generalization to positive cosmological constant, which has a finite 3-space and corresponds to a special case of a stiff fluid solution proposed by Buchdahl and Land and, later, by Iba\~nez and Sanz to model relativistic stars. However, there is a hidden cosmological constant and the peculiar geometry prevents the use of this spacetime to model relativistic stars.

Analytical scalar field solutions on Lifshitz spacetimes

In this work, we investigate the existence of analytic solutions of static scalar fields on Lifshitz spacetimes. We evade Derrick's theorem on curved spacetimes by breaking general covariance and use first-order formalism to obtain solutions with finite energy related to the time-translational invariance of the background geometry along with the energy-momentum tensor of the model. We show that such solutions exist and are stable in systems where the Lifshitz background geometry is fixed and the self-interaction potential of the scalar field explicitly depends on the radial coordinate present in the metric.

Disformal mappings of spherical DHOST geometries

New solutions of DHOST theories can be generated by applying adisformal tranformation to a known seed solution. We examine the nature ofspherically symmetric solutions of DHOST gravity obtained by disformingstatic spherical scalar field solutions, or stealth solutions, of generalrelativity. It is shown that, in these cases, black hole horizons arenever created by disforming a black hole seed. New DHOST solutions arethen created by disforming two lesser known scalar field solutions ofgeneral relativity: Wyman's “other” solution and theHusain-Martinez-Nuñez one. These new solutions demonstrate that one canobtain black hole horizons, wormhole throats, or horizonless geometries bydisforming non-stealth, time-dependent, seeds.