Charged Scalar Field Research Articles

Vacuum currents in curved tubes

We investigate the combined effects of spatial curvature and topology on the properties of the vacuum state for a charged scalar field localized on rotationally symmetric 2D curved tubes. For a general spatial geometry and for quasiperiodicity condition with a general phase, the representation of the Hadamard function is provided where the topological contribution is explicitly extracted. As an important local characteristic of the vacuum state the expectation value of the current density is studied. The vacuum current is a periodic function of the magnetic flux enclosed by the tube with the period of flux quantum. The general formula is specified for constant radius and conical tubes. As another application, we consider the Hadamard function and the vacuum current density for a scalar field on the Beltrami pseudosphere. Several representations are provided for the corresponding expectation value. For small values of the proper radius of the tube, compared with the curvature radius, the effect of spatial curvature on the vacuum current is weak and the leading term in the corresponding expansion coincides with the current density on a constant radius tube. The effect of curvature is essential for proper radii of the tube larger than the radius of spatial curvature. In this limit the falloff of the current density, as a function of the proper radius, follows a power law for both massless and massive fields. This behavior is in clear contrast to the one for a constant radius tube with exponential decay for massive fields. We also compare the vacuum currents on the Beltrami pseudosphere and on locally de Sitter and anti–de Sitter 2D tubes. Published by the American Physical Society 2024

Page curves in holographic superconductors

Considering a doubly holographic model, we study the black hole information paradox for the eternal AdSd-RN black hole coupled to and in equilibrium with a d-dimensional conformal bath whose state has been deformed by the charged scalar field coupled to a U(1) gauge field. Without a brane, the spontaneous symmetry breaking of the gauge field on boundary systems can induce a second-order phase transition of the charged scalar field at the critical temperature, known as holographic superconductors. The bath deformation can significantly change its entanglement dynamics with the black hole, resulting in variations in the Page curve and Page time. Our results indicate that characteristic parameters of the Page curve, such as entanglement velocity, initial area difference and Page time, can be used as suitable probes to detect superconducting phase transitions. In particular, the entanglement velocity can also probe both Kasner flows and Josephson oscillations. When keeping the endpoint of the radiation region fixed at twice the critical Page point, the entanglement velocity (the internal backreaction) has a more significant influence on the Page time compared to the initial area difference (the external backreaction). Published by the American Physical Society 2024

Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged N-component scalar fields and SO(N) symmetry.

We consider a three-dimensional lattice Abelian Higgs gauge model for a charged N-component scalar field ϕ, which is invariant under SO(N) global transformations for generic values of the parameters. We focus on the strong-coupling regime, in which the kinetic Hamiltonian term for the gauge field is a small perturbation, which is irrelevant for the critical behavior. The Hamiltonian depends on a parameter v, which determines the global symmetry of the model and the symmetry of the low-temperature phases. We present renormalization-group predictions, based on a Landau-Ginzburg-Wilson effective description that relies on the identification of the appropriate order parameter and on the symmetry-breaking patterns that occur at the strong-coupling phase transitions. For v=0, the global symmetry group of the model is SU(N); the corresponding model may undergo continuous transitions only for N=2. For v≠0, i.e., in the SO(N) symmetric case, continuous transitions (in the Heisenberg universality class) are possible also for N=3 and 4. We perform Monte Carlo simulations for N=2,3,4,6, to verify the renormalization-group predictions. Finite-size scaling analyses of the numerical data are in full agreement.

Charge superradiance on charged BTZ black holes

We study superradiant scattering for a charged scalar field subject to Robin (mixed) boundary conditions on a charged BTZ black hole background. Scalar field modes having a real frequency do not exhibit superradiant scattering, independent of the boundary conditions applied. For scalar field modes with a complex frequency, no superradiant scattering occurs if the black hole is static. After exploring some regions of the parameter space, we provide evidence for the existence of superradiantly scattered modes with complex frequencies for a charged and rotating BTZ black hole. Most of the superradiantly scattered modes we find satisfy Robin (mixed) boundary conditions, but there are also superradiantly scattered modes with complex frequencies satisfying Dirichlet and Neumann boundary conditions. We explore the effect of the black hole and scalar field charge on the outgoing energy flux of these superradiantly scattered modes, and also investigate their stability.

Zeroth and second laws of black hole mechanics in Einstein-Maxwell-scalar effective field theory

There has been recent progress in extending the zeroth and second laws of black hole mechanics to gravitational effective field theories (EFTs). We generalize these results to a much larger class of EFTs describing gravity coupled to electromagnetism and a real scalar field. We also show that the zeroth law holds for the EFT of gravity coupled to electromagnetism and a charged scalar field. Published by the American Physical Society 2024

Electric traversable wormhole supported by a charged scalar field

Electric traversable wormhole supported by a charged scalar field

No scalar-haired Cauchy horizon theorem in charged Gauss–Bonnet black holes

Recently, a “no inner (Cauchy) horizon theorem” for static black holes with non-trivial scalar hairs has been proved in Einstein–Maxwell–scalar theories and also in Einstein–Maxwell–Horndeski theories with the non-minimal coupling of a charged (complex) scalar field to Einstein tensor. In this paper, we study an extension of the theorem to the static black holes in Einstein–Maxwell–Gauss–Bonnet-scalar theories, or simply, charged Gauss–Bonnet (GB) black holes. We find that no inner horizon with charged scalar hairs is allowed for the planar (k=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=0$$\\end{document}) black holes, as in the case without GB term. On the other hand, for the non-planar (k=±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=\\pm 1$$\\end{document}) black holes, we find that the haired inner horizon can not be excluded due to GB effect generally, though we can not find a simple condition for its existence. As some explicit examples of the theorem, we study numerical GB black hole solutions with charged scalar hairs and Cauchy horizons in asymptotically anti-de Sitter space, and find good agreements with the theorem. Additionally, in an Appendix, we prove a “no-go theorem” for charged de Sitter black holes (with or without GB terms) with charged scalar hairs in arbitrary dimensions.

Vacuum Currents for a Scalar Field in Models with Compact Dimensions

This paper presents a review of investigations into the vacuum expectation value of the current density for a charged scalar field in spacetimes that hold toroidally compactified spatial dimensions. As background geometries, the locally Minkowskian (LM), locally de Sitter (LdS), and locally anti-de Sitter (LAdS) spacetimes are considered. Along compact dimensions, quasi-periodicity conditions are imposed on the field operator and the presence of a constant gauge field is assumed. The vacuum current has nonzero components along the compact dimensions only. Those components are periodic functions of the magnetic flux enclosed in compact dimensions, with a period that is equal to the flux quantum. For LdS and LAdS geometries, and for small values of the length of a compact dimension, compared with the curvature radius, the leading term in the expansion of the the vacuum current along that dimension coincides with that for LM bulk. In this limit, the dominant contribution to the mode sum for the current density comes from the vacuum fluctuations with wavelengths smaller to those of the curvature radius; additionally, the influence of the gravitational field is weak. The effects of the gravitational field are essential for lengths of compact dimensions that are larger than the curvature radius. In particular, instead of the exponential suppression of the current density in LM bulk, one can obtain a power law decay in the LdS and LAdS spacetimes.

Charged scalar field propagator under an external magnetic field: a connection between eigenfunction and proper time methods

Charged scalar field propagator under an external magnetic field: a connection between eigenfunction and proper time methods

Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String

In this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a (1+D)-dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis, we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to develop this analysis, we obtain the complete set of normalized positive-energy solutions of the Klein–Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in the presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary-induced vacuum polarization effects for both field squared and the energy–momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of a cosmic string and boundary induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated.

Overcharging an accelerating Reissner-Nordström-anti-de Sitter black hole with test field and particle

Accelerating black holes have been widely studied in the context of black hole thermodynamics, holographic gravity theories, and in the description of black holes at the center of galaxies. As a fundamental assumption to ensure spacetime causality, we investigate the weak cosmic censorship conjecture (WCCC) in the accelerating Reissner-Nordström-Anti-de Sitter (RN-AdS) spacetime through the scattering of a charged field and the absorption of a charged particle. For the scattering of a charged scalar field, both near-extremal and extremal accelerating RN-AdS black holes cannot be overcharged, thereby upholding the validity of the WCCC. In the case of the absorption of a test charged particle, the results demonstrate that the event horizon of the extremal accelerating RN-AdS black hole cannot be destroyed, while the event horizon of the near-extremal black hole can be overcharged if the test particle satisfies certain conditions. The above results suggest that, in the case of test particles, second-order effects like self-force and self-energy should be further considered.

Noncommutative scalar field theory in a curved background: Duality between noncommutative and effective commutative description

We study a noncommutative (NC) deformation of a charged scalar field, minimally coupled to a classical (commutative) Reissner–Nordström-like background. The deformation is performed via a particularly chosen Killing twist to ensure that the geometry remains undeformed (commutative). An action describing a NC scalar field minimally coupled to the RN geometry is manifestly invariant under the deformed [Formula: see text] gauge symmetry. We find the equation of motion and conclude that the same equation is obtained from the commutative theory in a modified geometrical background described by an effective metric. This correspondence we call “duality between formal and effective approach”. We also show that a NC deformation via semi-Killing twist operator cannot be rewritten in terms of an effective metric. There is dual description for those particular deformations.

Hyperbolic field theory as a Lorentz covariant description for the dissipation

Based on the extension of the space of solutions for the D’Alambertian operator on the hyperbolic complex plane, we construct a formalism for the dissipative dynamics of two charged scalar fields, with explicit internal and background Lorentz symmetries, as opposed to the well-established scheme based on damping oscillators physics, which breaks down explicitly such a symmetry. The hyperbolic extension implies that the usual U(1) symmetry for charged scalar fields is extended with the incorporation of a non-compact SO(1,1) symmetry that will allow to describe the damping effects. As response properties of the interaction, the dissipation coefficients in time and in space are determined in the frequency-momentum space; the regimes with and without gapped energy–momentum states emerge; additionally the partition function and an entangled state generated by the dissipation are constructed. The pair of charged fields can be identified with field theories on asymptotic boundaries of gravitational backgrounds, and the possible holographic scenarios are discussed.

Quantum absorption properties of Kerr–Newman–de Sitter black hole

In this work, we utilize the Wentzel–Kramers–Brillouin (WKB) approximation to determine the Hawking temperature corresponding to the Kerr–Newman–de Sitter (KNdS) spacetime. Specifically, we calculate the low frequency absorption cross-section for the KNdS black hole in a charged scalar field and analyzed its dependence on the characteristics of the black hole. Through our research, we have established a correlation between the absorption cross-section ([Formula: see text]) and the Hawking temperature ([Formula: see text]) of the black hole, demonstrating an inverse proportionality between the two quantities. Furthermore, we also deduce the absorption cross-sections for Kerr–de Sitter, Reissner–Nordstrom–de Sitter, Schwarzschild–de Sitter and Schwarzschild black holes, and compare them with previously obtained results. The validity of our findings is demonstrated by these comparisons.

Vacuum polarization induced by a cosmic string and a brane in AdS spacetime

In this paper we investigate the vacuum polarization effects associated to a charged quantum massive scalar field on a (D+1)-dimensional anti-de Sitter background induced by a magnetic-flux-carrying cosmic string in the braneworld model context. We consider the brane parallel to the anti-de Sitter boundary and the cosmic string orthogonal to them. Moreover, we assume that the field obeys the Robin boundary condition on the brane. Because the brane divides the space into two regions with different properties of the quantum vacuum, we calculate the vacuum expectation value (VEV) of the field squared and the energy–momentum tensor (EMT) in each region. To develop these analyses, we have constructed the positive frequency Wightman function for both regions. The latter is decomposed in a part associated with the anti-de Sitter bulk in the presence of a cosmic string only, and the other part induced by the brane. The vacuum polarization effects associated with the higher-dimensional anti-de Sitter bulk in the presence of cosmic string have been developed in the literature, and here we are mainly interested in the effects induced by the brane. We show that the VEVs of the field squared and the components of the EMT induced by the cosmic string are finite on the brane. Explicitly, we compare these observables with the corresponding ones induced by the brane only, and show that near the brane the contribution induced by the latter is larger than the one induced by the string; however, for points distant from the brane the situation is reversed. Moreover, some asymptotic expressions for the VEV of the field squared and EMT are provided for specific limiting cases of the physical parameters of the model. Also, an application of our results is given for a cosmic string in the Z_2-symmetric Randall–Sundrum braneworld model with a single brane.

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

Global Stability for Charged Scalar Fields in an Asymptotically Flat Metric in Harmonic Gauge

We prove global stability for the charged scalar field system on a background spacetime, which is close to 1+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1+3$$\\end{document}-dimensional Minkowski space and whose outward light cones converge to those for the Schwarzs-child metric at null infinity. The key technique to this proof is the use of a modified null frame, depending only on the mass M of the metric, which captures the asymptotic behavior of the metric at future null infinity. Our results are analogous to results obtained in Minkowski space by Lindblad and Sterbenz in (IMRP Int Math Res Pap 2006:52976, 2006) up to a change in coordinates, and will in the sequel be used to prove the full structure of the Einstein–charge scalar field system in these modified harmonic coordinates.

Spectral properties for the Klein-Gordon Hamiltonian in charged black hole backgrounds

Charged massive scalar fields on charged black hole backgrounds are investigated through methods of spectral analysis in Krein spaces. We consider, on the three charged black hole backgrounds (Nariai, Reissner-Nordström, ultracold-II) taken into account, a necessary condition for the existence of complex eigenvalues. We show that even if it is satisfied, in two cases (Nariai and ultracold-II), by direct calculation, they actually cannot exist. In both cases, the Klein paradox occurs without restriction on the parameters. In the third case, the condition for their existence is shown to coincide with the condition, allowing the quantum discharge phenomenon associated with the Klein paradox. We also clarify the role of “classical potentials,” which appear in the physical literature on the subject, giving rise to the so-called level-crossing appearing in semiclassical calculations, and we comment on problems occurring in quantum field theory in the presence of complex eigenvalues.

Electroweak baryogenesis between broken phases in multi-step phase transition

Possibility of electroweak baryogenesis (EWBG) via multi-step phase transition (PT) is considered. We investigate the EWBG between SU(2) broken phases in the second step PT of the two-step PT. The produced baryon number asymmetry is evaluated using a prototypical model with a SU(2) charged CP-odd scalar field. We show that the second step PTs where the sphaleron rate is possible to be un-suppressed before the PTs, which can reproduce the sufficient baryon number asymmetry. Our studies can be adapted to models with extra SU(2) scalar fields. We discuss specific models suitable for our scenario.

Late-time asymptotics for geometric wave equations with inverse-square potentials

We introduce a new, physical-space-based method for deriving the precise leading-order late-time behaviour of solutions to geometric wave equations on asymptotically flat spacetime backgrounds and apply it to the setting of wave equations with asymptotically inverse-square potentials on Schwarzschild black holes. This provides a useful toy model setting for introducing methods that are applicable to more general linear and nonlinear geometric wave equations, such as wave equations for electromagnetically charged scalar fields, wave equations on extremal Kerr black holes and geometric wave equations in even space dimensions, where existing proofs for deriving precise late-time asymptotics might not apply. The method we introduce relies on exploiting the spatial decay properties of time integrals of solutions to derive the existence and precise genericity properties of asymptotic late-time tails and obtain sharp, uniform decay estimates in time.