Scalar Field Research Articles

The Kerr–Bumblebee exact massive and massless scalar quasibound states and Hawking radiation

In this letter, we will focus on the Klein–Gordon equation with rotating axially symmetric black hole solution of the Einstein–Bumblebee theory, so called the Kerr–Bumblebee black hole, as its 3 + 1 background space-time. We start with constructing the covariant Klein–Gordon equation component by component and with the help of the ansatz of separation of variables, we successfully separate the polar part and found the exact solution in terms of Spheroidal Harmonics while the radial exact solution is discovered in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that is resulted in a complex-valued energy levels expression for a massive scalar field, where the real part is the scalar particle’s energy while the imaginary part represents the quasibound stats’s decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe the decaying nature of the relativistic scalar field bound in the curved Kerr–Bumblebee space-time. We also investigate the Hawking radiation of the Kerr–Bumblebee black hole’s apparent horizon via the Damour–Ruffini method by making use the obtained exact scalar’s wave functions. The radiation distribution function and the Hawking temperature are successfully obtained.

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

Towards geodesic ridge curve for region-wise linear representation of geodesic distance field

This paper addresses the challenge of representing geodesic distance fields on triangular meshes in a piecewise linear manner. Unlike general scalar fields, which often assume piecewise linear changes within each triangle, geodesic distance fields pose a unique difficulty due to their non-differentiability at ridge points, where multiple shortest paths may exist. An interesting observation is that the geodesic distance field exhibits an approximately linear change if each triangle is further decomposed into sub-regions by the ridge curve. However, computing the geodesic ridge curve is notoriously difficult. Even when using exact algorithms to infer the ridge curve, desirable results may not be achieved, akin to the well-known medial-axis problem. In this paper, we propose a two-stage algorithm. In the first stage, we employ Dijkstra's algorithm to cut the surface open along the dual structure of the shortest path tree. This operation allows us to extend the surface outward (resembling a double cover but with distinctions), enabling the discovery of longer geodesic paths in the extended surface. In the second stage, any mature geodesic solver, whether exact or approximate, can be employed to predict the real ridge curve. Assuming the fast marching method is used as the solver, despite its limitation of having a single marching direction in a triangle, our extended surface contains multiple copies of each triangle, allowing various geodesic paths to enter the triangle and facilitating ridge curve computation. We further introduce a simple yet effective filtering mechanism to rigorously ensure the connectivity of the output ridge curve. Due to its merits, including robustness and compatibility with any geodesic solver, our algorithm holds great potential for a wide range of applications. We demonstrate its utility in accurate geodesic distance querying and high-fidelity visualization of geodesic iso-lines.

Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics

We develop a model of spatially flat, homogeneous and isotropic cosmology in Lorentzian Regge calculus, employing four-dimensional Lorentzian frusta as building blocks. By examining the causal structure of the discrete spacetimes obtained by gluing such four-frusta in spatial and temporal direction, we find causality violations if the sub-cells connecting spatial slices are spacelike. A Wick rotation to the Euclidean theory can be defined globally by a complexification of the variables and an analytic continuation of the action. Introducing a discrete free massless scalar field, we study its equations of motion and show that it evolves monotonically. Furthermore, in a continuum limit, we obtain the equations of a homogeneous scalar field on a spatially flat Friedmann background. Vacuum solutions to the causally regular Regge equations are static and flat and show a restoration of time reparametrisation invariance. In the presence of a scalar field, the height of a frustum is a dynamical variable that has a solution if causality violations are absent and if an inequality relating geometric and matter boundary data is satisfied. Edge lengths of cubes evolve monotonically, yielding a contracting or an expanding branch of the Universe. In a small deficit angle expansion, the system can be deparametrised via the scalar field and a continuum limit of the discrete theory can be defined which we show to yield the relational Friedmann equation. These properties are obstructed if higher orders of the deficit angle are taken into account. Our results suggest that the inclusion of timelike sub-cells is necessary for a causally regular classical evolution in this symmetry restricted setting. Ultimately, this works serves as a basis for forthcoming investigations on the cosmological path integral within the framework of effective spin foams.

Quantum Brownian motion induced by a scalar field in Einstein’s universe

The Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless real scalar field in Einstein’s universe is studied. By assuming the small displacement condition, the dispersion in the momentum and position of a point particle coupled to the massless scalar field are obtained. As a consequence of the homogeneity and isotropy properties of the Einstein’s Universe, we find that all components of these physical observables are identical. We also examine divergent behaviors associated with the physical momentum and position dispersions, which we attribute to the IR1×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{1}\ imes $$\\end{document}S3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}$$\\end{document} compact topology of Einstein’s universe. Finally, based on the small displacement condition assumed, we analyze the limit of validity of our investigation.

Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields.

We investigate the nature of the deconfinement transitions in three-dimensional lattice Abelian Higgs models, in which a complex scalar field of integer charge Q≥2 is minimally coupled with a compact U(1) gauge field. Their phase diagram presents two phases separated by a transition line where static charges q, with q<Q, deconfine. We argue that these deconfinement transitions belong to the same universality class as transitions in generic three-dimensional Z_{Q} gauge models. In particular, they are Ising-like for Q=2, of first order for Q=3, and belong to the three-dimensional gauge XY universality class for Q≥4. This general scenario is supported by numerical finite-size scaling analyses of the energy cumulants for Q=2,Q=4, and Q=6.

Learned Inference of Annual Ring Pattern of Solid Wood

AbstractWe propose a method for inferring the internal anisotropic volumetric texture of a given wood block from annotated photographs of its external surfaces. The global structure of the annual ring pattern is represented using a continuous spatial scalar field referred to as the growth time field (GTF). First, we train a generic neural model that can represent various GTFs using procedurally generated training data. Next, we fit the generic model to the GTF of a given wood block based on surface annotations. Finally, we convert the GTF to an annual ring field (ARF) revealing the layered pattern and apply neural style transfer to render orientation‐dependent small‐scale features and colors on a cut surface. We show rendered results of various physically cut real wood samples. Our method has physical and virtual applications such as cut‐preview before subtractive fabricating solid wood artifacts and simulating object breaking.

Quasinormal Spectrum of (2+1)$(2+1)$‐Dimensional Asymptotically Flat, dS and AdS Black Holes

AbstractWhile ‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher resembles that in four‐dimensional spacetime with the corresponding asymptotic.

On the string landscape without hypermultiplets

In this work we study interesting corners of the quantum gravity landscape with 8 supercharges pushing the boundaries of our current understanding. Calabi-Yau threefolds compactifications of F/M/type II theories to 6, 5 and 4 dimensions are the most prominent examples of this class, and these always lead to a universal hypermultiplet coming from the volume/string coupling constant. We find new examples of asymmetric orbifold constructions which have no hypermultiplets in 4 or 5 dimensions and no neutral hypers in 6d. We argue that these theories can also be obtained by going to strong coupling/small volume regions of geometric constructions where a new Coulomb branch opens up and moving in this direction freezes the volume/string coupling constant. Interestingly we find that the Kodaira condition encountered in geometric limits of F-theory compactifications to 6 dimensions is violated in these corners of the landscape due to strong quantum corrections. We also construct a theory in 3 dimensions which if it were to arise by toroidal compactifications from 5d, it would have to come from pure N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supergravity with no massless scalar fields.

Frozen Gaussian sampling for scalar wave equations

Frozen Gaussian sampling for scalar wave equations

The solution of the nonlinear Poisson-Boltzmann equation using lattice-Boltzmann

In this paper we present the solution of the Poisson-Boltzmann equation using the Lattice-Boltzmann method. In order to obtain the solution, we use a redefinition of tensor n°, which is declared as a symmetric tensor whose diagonal components are chosen as the second derivative in time of the first moment of the distribution function, and the components outside of the diagonal give account of the nonlinear terms. The results are presented in two dimensions employing the D2Q9 lattice velocity scheme. We obtain results for the scalar field and its gradient for several kinds of initial conditions.

Einstein gravity as the thermal equilibrium state of a nonminimally coupled scalar field geometry

Einstein gravity as the thermal equilibrium state of a nonminimally coupled scalar field geometry

What should we understand by the four-momentum of physical system?

It is shown that, in general, in curved spacetime, none of the known definitions of four-momentum correspond to the definition, in which all the system’s particles and fields, including fields outside matter, make an explicit contribution to the four-momentum. This drawback can be eliminated under the assumption that the primary representation of four-momentum is the sum of two nonlocal four-vectors of the integral type with covariant indices. The first of these four-vectors is the generalized four-momentum, found with the help of Lagrangian density. The time component of the generalized four-momentum, in theory of vector fields, is proportional to the particles’ energy in scalar field potentials, and the space component is related to vector field potentials. The second four-vector is the four-momentum of fields themselves, and its time component is related to the energy given by tensor invariants. As a result, the system’s four-momentum is defined as a four-vector with a covariant index. The standard approach makes it possible to find the four-momentum in covariant form only for a free point particle. In contrast, the obtained formulas for calculating the four-momentum components are applied to a stationary and moving relativistic uniform system, consisting of many particles. In this case, the main fields of the system under consideration are taken into account, including the electromagnetic and gravitational fields, the acceleration field and the pressure field. All these fields are considered vector fields, which makes it possible to unambiguously determine the equations of motion of the fields themselves and the equations of motion of matter in these fields. The formalism used includes the principle of least action, charged and neutral four-currents, corresponding four-potentials and field tensors, which ensures unification and the possibility of combining fields into a single interaction. Within the framework of the special theory of relativity, it is shown that due to motion, the four-momentum of the system increases in proportion to the Lorentz factor of the system’s center of momentum, while in the matter of the system the sum of the energies of all fields is equal to zero. The calculation of the integral vector’s components in the relativistic uniform system shows that the so-called integral vector is not equal to four-momentum and is not a four-vector at all, although it is conserved in a closed system. Thus, in the theory of relativistic vector fields, the four-momentum cannot be found with the help of an integral vector and components of the system’s stress-energy tensor, in contrast to how it is assumed in the general theory of relativity.

An optimized basis for hadronic light-by-light scattering

We present a new basis for the hadronic light-by-light (HLbL) tensor that is optimized for the evaluation of narrow-resonance contributions to HLbL scattering in the anomalous magnetic moment of the muon. As main advantage, kinematic singularities are manifestly absent for pseudoscalar, scalar, and axial-vector states, while the remaining singularities for tensor resonances are minimized, even avoided for special cases, and simple crossing relations among the scalar functions maintained. We scrutinize the properties of this new basis for the scalar-QED pion box, demonstrating that the partial-wave convergence even slightly improves compared to our previous work, and discuss the physical sum rules that ensure basis independence of the HLbL contribution. Finally, we provide explicit expressions for narrow (pseudo-)scalar, axial-vector, and tensor intermediate states in terms of their respective transition form factors.

Asimulation: Domain formation and impact on observables in resolved cosmological simulations of the (a)symmetron

The symmetron is a dark energy and dark matter candidate that forms topological defects in the late-time universe and holds the promise of resolving some of the cosmological tensions. We performed high-resolution simulations of the dynamical and non-linear (a)symmetron using the recently developed relativistic N-body code asevolution. By extensively testing the temporal and spatial convergence of domain decompositioning and domain wall stability, we determined criteria and physical intuition for the convergence. We applied the resolution criteria to run five high-resolution simulations with $1280^3$ grids and a box size of $500$ Mpc/h of the (a)symmetron . W e considered the behaviour of the scalar field and the domain walls in each scenario. We find the effect on the matter power spectra, the HMFs, and observables computed over the past light cone of an observer, such as the integrated Sachs-Wolfe and non-linear Rees-Sciama effect and the lensing, compared to Lambda CDM. We show local oscillations of the fifth force strength and the formation of planar structures in the density field. The dynamics of the field was visualised in animations with high resolution in time. The simulation code is made publicly available.

Screwon spectral statistics and dispersion relation in the quantum Rajeev–Ranken model

The Rajeev–Ranken (RR) model is a Hamiltonian system describing screw-type nonlinear waves (screwons) of wavenumber k in a scalar field theory pseudodual to the 1+1D SU(2) principal chiral model. Classically, the RR model based on a quadratic Hamiltonian on a nilpotent/Euclidean Poisson algebra is Liouville integrable. Upon adopting canonical variables in a slightly extended phase space, the model was interpreted as a novel 3D cylindrically symmetric quartic oscillator with a rotational energy. Here, we examine the spectral statistics and dispersion relation of quantized screwons via numerical diagonalization validated by variational and perturbative approximations. We also derive a semiclassical estimate for the cumulative level distribution which compares favorably with the one from numerical diagonalization. The spectrum shows level crossings typical of an integrable system. The ith unfolded nearest neighbor spacings are found to follow Poisson statistics for small i. Nonoverlapping spacing ratios also indicate that successive spectral gaps are independently distributed. After displaying universal linear behavior over energy windows of short lengths, the spectral rigidity saturates at a length and value that scales with the square-root of energy. For strong coupling λ and intermediate k, we argue that reduced screwon energies can depend only on the product λk. Numerically, we find power law dependences on λ and k with an approximately common exponent 2/3 provided the angular momentum quantum number l is small compared to the number of nodes n in the radial wavefunction. On the other hand, for the ground state n=l=0, the common exponent becomes 1.

Conformal diagrams for stationary and dynamical strong-field hyperboloidal slices

Conformal Carter–Penrose diagrams are used for the visualization of hyperboloidal slices, which are smooth spacelike slices reaching null infinity. The focus is on the Schwarzschild black hole geometry in spherical symmetry, whose Penrose diagrams are introduced in a pedagogical way. The stationary regime involves time-independent slices. In this case, different options are given for integrating the height function—the main ingredient for constructing hyperboloidal foliations. The dynamical regime considers slices changing in time, which are evolved together with the spacetime using the eikonal equation. It includes the relaxation of hyperboloidal Schwarzschild trumpet slices and the collapse of a massless scalar field into a black hole, for which Penrose diagrams are presented.

Weak cosmic censorship conjecture and black hole shadow for black hole with generalized uncertainty principle

Based on string theory, loop quantum gravity, black hole physics, and other theories of quantum gravity, physicists have proposed generalized uncertainty principle (GUP) modifications. In this work, within the framework of GUP gravity theory, we successfully derive an exact solution to Einstein’s field equation, and discuss the possibility of using EHT to test GUP and how GUP changes the weak cosmic censorship conjecture for black holes. We analyze two different ways of constructing GUP rotating black holes (model I and model II). Model I takes into account the modification of mass by GUP, i.e., the change in mass by quantization of space, and the resulting GUP rotating black hole metric (18) is similar in form to the Kerr black hole metric. Model II takes into account the modification of the rotating black hole when GUP is an external field, where GUP acts like an electric charge, and the resulting GUP rotating black hole metric (19) is similar in form to the Kerr–Newman black hole metric. The difference between (18) and (19) in the spacetime linear structure provides a basis for us to examine the physical nature of GUP rotating black holes from observation. By analyzing the shadow shape of the GUP rotating black hole, we discover intriguing characteristics regarding the impact of first-order and second-order momentum correction coefficients on the black hole’s shadow shape. These findings will be instrumental in future GUP testing using EHT. Additionally, by incident test particle and scalar field with a rotating GUP black hole, the weak cosmic censorship conjecture is not violated in either extreme black holes or near-extreme black holes.

Asymptotically AdS black hole with a conformally-coupled scalar field in the first-order formalism of gravity

Asymptotically AdS black hole with a conformally-coupled scalar field in the first-order formalism of gravity

Modeling of self-gravitating compact configurations using radial metric deformation approach

This study analyzes new analytical solution types that explore the influence of complexity on time-independent, spherically symmetric astrophysical configurations, based on a radial metric deformation scheme also known as minimal geometric deformation. We demonstrate that the complexity factor, a scalar function obtained via splitting the Riemann tensor orthogonally, exhibits an additive property. This implies that the overall complexity of a system containing two interacting fluid distributions (represented by Tμν and Φμν) is simply the sum of the individual complexities of each fluid. This work employs the radial metric deformation approach, a powerful tool for constructing astrophysically viable models of anisotropic matter, by building upon the Vaidya–Tikekar and Finch–Skea relativistic spacetimes. We observe that both the metric ansatzes produce qualitatively similar features, though the magnitudes may vary slightly, for any non-zero value of the decoupling parameter (0≤α<1). Interestingly, both models preserve their anisotropic nature despite reaching the zero-complexity limit (α=1). Finally,we delve into the physical implications of these novel solution types, examining their potential to accurately represent real compact configurations.