Scalar Field Research Articles

Black hole no-hair theorem for self-gravitating time-dependent spherically symmetric multiple scalar fields

We prove under certain weak assumptions a black hole no-hair theorem in spherically symmetric spacetimes for self-gravitating time-dependent multiple scalar fields with an arbitrary target space admitting a Killing field with a non-empty axis and arbitrary non-negative potential invariant under the flow of the Killing field. It is shown that for such configurations the only spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multi-scalar map. In due course of the proof we also unveil the intrinsic connection of the time-dependence of the scalar fields with the symmetries of the target space.

Testing the weak cosmic censorship conjecture in short haired black holes

The weak cosmic censorship conjecture is a hypothesis about the nature of event horizons and singularities during the formation of black holes. It posits that singularities are always enveloped by the event horizons of black holes, thereby preventing naked singularities from affecting the causal structure of spacetime. In this paper, we study the effect of rotating short haired black holes on the weak cosmic censorship conjecture. Discussion of whether the event horizons of a rotating short haired black hole is disrupted by studying incident neutral test particles and scalar fields. In the context of short haired black holes, when incident neutral test particles are considered for extreme and near extreme cases, our research results indicate that neutral test particles can destroy the event horizons of short haired black holes, violating the weak cosmic censorship conjecture. In the case of scalar field incidence in short haired black holes, for extreme situations, when the incident wave modes fall within the range of 12κM+βMκ<ωm<12Mκ+βMκ-12κ,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{1}{2\\kappa M+\\frac{\\beta }{M\\kappa }}<\\frac{\\omega }{m}<\\frac{1}{2M\\kappa + \\frac{\\beta }{M\\kappa }-\\frac{1}{2\\kappa }},$$\\end{document} the results indicate that the event horizons of rotating short haired black holes is disrupted. For near extreme cases, the presence of hair allows for the disruption of the event horizons of rotating short haired black holes, as indicated by our results. Therefore, these conclusions are intriguing and will provide new insights for us to further understand the weak cosmic censorship conjecture and explore the properties of short haired black holes.

The instability of the inner horizon of the quantum-corrected black hole

We analyse the stability of the inner horizon of the quantum-corrected black hole which is proposed in loop quantum gravity as the exterior of the quantum Oppenheimer–Snyder and Swiss Cheese models. It is shown that the flux and energy density of a test scalar field measured by free-falling observers are both divergent near the Cauchy horizon. By considering the generalized Dray–’t Hooft–Redmond relation which is independent of the field equation, we find that the mass inflation always happens and the scalar curvature and Kretschmann scalar are also divergent on the inner horizon. These suggest that the inner horizon is unstable and will probably turn into a null singularity.The results support the strong cosmic censorship hypothesis.However, this also implies that the quantum corrected model may not be the definitive endpoint as a regular black hole.Besides, it further proposes that it may be challenging to observe the astronomical phenomenon which depends on the existence of the inner horizon of the black hole

Signature of f(R) gravity via Lemaître–Tolman–Bondi inhomogeneous perturbations

We analyze inhomogeneous cosmological models in the local Universe, described by the Lemaître–Tolman–Bondi (LTB) metric and developed using linear perturbation theory on a homogeneous and isotropic Universe background. Focusing on the different evolution of spherical symmetric inhomogeneities, we compare the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}LTB model, in which the cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} is included in the LTB formalism, with inhomogeneous cosmological models based on fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} modified gravity theories viewed in the Jordan frame. We solve the system of field equations for both inhomogeneous cosmological models adopting the method of separation of variables: we integrate analytically the radial profiles of local perturbations, while their time evolution requires a numerical approach. The main result of the analysis concerns the different radial profiles of local inhomogeneities due to the presence of a non-minimally coupled scalar field in the Jordan frame of fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} gravity. While radial perturbations follow a power-law in the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}LTB model, Yukawa-like contributions appear in the fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} theory. Interestingly, this latter peculiar behavior of radial profile is not affected by the choice of the fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} functional form. The numerical solution of time-dependent perturbations exhibits a non-diverging profile. This work suggests that investigations about local inhomogeneities in the late Universe may allow us to discriminate if the present cosmic acceleration is caused by a cosmological constant term or a modified gravity effect.

Nonlocal coherence harvesting from quantum vacuum

Abstract It is well known that nonlocal coherence reflects nonclassical correlations better than quantum entan-&amp;#xD;glement. Here, we analyze nonlocal coherence harvesting from the quantum vacuum to particle detectors&amp;#xD;adiabatically interacting with a quantum scalar field in Minkowski spacetime. We find that the harvesting-&amp;#xD;achievable separation range of nonlocal coherence is larger than that of quantum entanglement. As the&amp;#xD;energy gap grows sufficiently large, the detectors harvest less quantum coherence, while the detectors could&amp;#xD;extract more quantum entanglement from the vacuum state. Compared with the linear configuration and the&amp;#xD;scalene configuration, we should choose the model of equilateral triangle configuration to harvest tripar-&amp;#xD;tite coherence from the vacuum. Finally, we find a monogamous relationship, which means that tripartite&amp;#xD;l1-norm of coherence is essentially bipartite types.

Asymptotically safe cosmology with non-canonical scalar field

Abstract We investigate the quantum modified cosmological dynamical equations in a Friedmann-Robertson-Walker universe filled with a barotropic fluid and a general non-canonical scalar field characterized by a Lagrangian similar to k-essence model but with a potential term. Quantum corrections are incorporated by considering the running of gravitational and potential couplings, employing the functional renormalization group approach. Covariant conservation of the non-canonical scalar field and the background barotropic fluid is considered separately, imposing a constraint resulting from the Bianchi identity. This constraint determines the evolution of the cut-off scale with the scale factor and also reveals cosmic fixed points, depending on whether the flow ceases or continues to evolve. We explore how the general non-canonical scalar field parameter affects the different types of cosmic fixed points and how it differs from the canonical case. Furthermore, we establish a bound on the ratio of the RG parameters involving the non-canonical parameter for which the universe may exhibit accelerated expansion for mixed fixed points. This bound indicates the non-canonical scalar field includes larger sets of RG fixed point which may give rise to an accelerated universe.

Hybrid meta/refractive lens design with an inverse design using physical optics

Hybrid lenses are created by combining metasurface optics with refractive optics, where refractive elements contribute optical power, while metasurfaces correct optical aberrations. We present an algorithm for optimizing metasurface nanostructures within a hybrid lens, allowing flexible interleaving of metasurface and refractive optics in the optical train. To efficiently optimize metasurface nanostructures, we develop a scalar field, ray-wave hybrid propagation method. This method facilitates the propagation of incident and derived adjoint fields through optical elements, enabling effective metasurface optimization within the framework of adjoint gradient optimization. Numerical examples of various lens configurations are presented to illustrate the versatility of the algorithm and showcase the benefits offered by the proposed approach, allowing metasurfaces to be positioned beyond the image space of a lens. Taking a F/2, 40° field-of-view, midwave infrared lens as an example, the lens exhibits an average focusing efficiency of 38% before the integration of metasurfaces. Utilizing the new algorithm to design two metasurfaces—one in the object space and one in the image space—results in significant enhancement of the average focusing efficiency to over 90%. In contrast, a counterpart design with both metasurfaces limited to the image space yields a lower average focusing efficiency of 73%.

Moderately dense granular gas of inelastic rough spheres

Abstract A kinetic theory for moderately dense gases of inelastic and rough spherical molecules is developed from &amp;#xD;the Enskog equation where a macroscopic state is characterised by 29 scalar fields which correspond to the moments of the distribution function: mass density, hydrodynamic velocity, pressure tensor, absolute temperature, translational and rotational heat fluxes, hydrodynamic angular velocity and angular velocity flux. The balance equations for the 29 scalar fields are obtained from a transfer equation derived from the Enskog equation where the kinetic and potential parts of the new moments of the distribution function and production terms are calculated from Grad's distribution function for the basic fields.&amp;#xD;The transition from the 29 field theory to an eight field theory -- with mass density hydrodynamic velocity, absolute temperature and hydrodynamic angular velocity -- leads to the determination of the transport coefficients of the Navier-Stokes and Fourier laws. The transport coefficients are functions of the normal and tangential restitution coefficients and of the local equilibrium radial distribution function. The transport coefficients in the limiting case of elastic rough spheres is also determined.

In-in correlators and scattering amplitudes on a causal set

Causal set theory is an approach to quantum gravity in which spacetime is fundamentally discrete at the Planck scale and takes the form of an irregular Lorentzian lattice, or “causal set,” from which continuum spacetime emerges in a large-scale (low-energy) approximation. In this work, we present new developments in the framework of interacting quantum field theory on causal sets. We derive a diagrammatic expansion for in-in correlators in local scalar field theories with finite polynomial interactions. We outline how these same correlators can be computed using the double-path integral, which acts as a generating functional for the in-in correlators. We modify the in-in generating functional to obtain a generating functional for in-out correlators. We define a notion of scattering amplitudes on causal sets with noninteracting past and future regions and verify that they are given by S-matrix elements (matrix elements of the time-evolution operator). We describe how these formal developments can be implemented to compute early Universe observables under the assumption that spacetime is fundamentally discrete. Published by the American Physical Society 2024

A phase-field model for the brittle fracture of Euler–Bernoulli beams coupling stretching and bending

Damage gradient models seek to simulate fracture mechanics by modulating the material stiffness. Within this framework, a singular scalar field representing damage is commonly utilized to globally decrease elastic energy. However, when considering structural models like beams and plates, this approach often fails to adequately capture important aspects due to the interaction between stretching and bending contributions. In this work, we propose a model for planar Euler–Bernoulli beams that incorporates the following features: firstly, we utilize two phase-field damage parameters to describe material damaging, specifically addressing the ‘erosion’ occurring above and below the original, undamaged beam; secondly, we assume a simple linear dependence of the axial stress field on the thickness coordinate, along with linear dependence on the axial force and bending moment. By appropriately identifying the constitutive response, our model effectively considers the coupling between stretching and bending induced during through-the-thickness damage, demonstrating good agreement with 2D observations.

Gravitating kinks with asymptotically flat metrics

Abstract In this work, we consider a two-dimensional (2D) dilaton gravity model where the dilaton kinetic term $\mathcal{X}$ is modified by an additional derivative coupling term $\alpha\mathcal{X}^2$. In the case with a canonical scalar matter field, the field equations of this model have a simple first-order formalism, from which exact static kink solutions can be constructed. The novelty of these solutions is that the corresponding metric can be asymptotically flat rather than asymptotically anti de Sitter. The linear stability and the localization of scalar matter fields are also studied. It was found that the solutions are stable against small linear perturbations, and the localization of scalar matter fields can be realized by introducing scalar-kink interactions.

Holographic renormalization of Horndeski gravity

We study the renormalization of a particular sector of Horndeski theory. In particular, we focus on the nonminimal coupling of a scalar field to the Gauss-Bonnet term and its kinetic coupling to the Einstein tensor. Adopting a power expansion on the scalar function that couples the Gauss-Bonnet term, we find specific conditions on their coefficients such that the action and charges are finite. To accomplish the latter, we add a finite set of intrinsic boundary terms. The contribution of the nonminimal coupling generates an effective scalar mass, allowing us to recover a modified Breitenlohner-Freedman bound. Furthermore, we compute the holographic 1-point functions and Ward identities associated with the scalar field and the metric. We constrain the parameter space of the theory by taking into account the preservation of scaling symmetry at the boundary.

Analysis of two interactive burning droplets with different temperatures

This paper presents a comprehensive theoretical analysis of the interaction between two quasi-steady burning droplets with differing temperatures, sizes and distances, building upon the mass-flux-potential model and flame-sheet assumption. In contrast to existing research, this study introduces a fresh perspective on droplet interactions by considering the different temperatures of the droplets. Utilizing the bispherical coordinate approach, theoretical solutions for the Stefan flow, scalar fields, droplet evaporation/burning rates, interaction coefficients and flame positions have been derived successfully. A comparison with extensive numerical simulations indicates a good agreement between the analytical and numerical results under a variety of conditions. It is revealed that proximity between the droplets causes non-uniform evaporation rates on their surfaces, and in some cases, leads to condensation on the cooler droplet. Notably, when the temperatures of the two droplets differ, this results in an uneven temperature distribution across the flame surface, and increasing the temperature of one droplet substantially elevates the temperature of the nearby flame. This study also establishes a criterion for the transition between different combustion modes, specifically between group and separated combustion. The findings of this study are crucial in deepening our understanding of evaporation and combustion processes, as well as the dynamics of flame spreading, local ignition, and extinction in systems involving multiple droplets.

Perturbations of spinning black holes in dynamical Chern-Simons gravity: Slow rotation equations

The detection of gravitational waves resulting from the coalescence of binary black holes by the LIGO-Virgo-Kagra Collaboration has inaugurated a new era in gravitational physics. These gravitational waves provide a unique opportunity to test Einstein’s general relativity and its modifications in the regime of extreme gravity. A significant aspect of such tests involves the study of the ringdown phase of gravitational waves from binary black hole coalescence, which can be decomposed into a superposition of various quasinormal modes. In general relativity, the spectra of quasinormal modes depend on the mass, spin, and charge of the final black hole, but they can also be influenced by additional properties of the black hole spacetime, as well as corrections to the general theory of relativity. In this work, we focus on a specific modified theory known as dynamical Chern-Simons gravity. We employ the modified Teukolsky formalism developed in a previous study and lay down the foundations to investigate perturbations of slowly rotating black holes admitted by the theory. Specifically, we derive the master equations for the Ψ0 and Ψ4 Weyl scalar perturbations that characterize the radiative part of gravitational perturbations, as well as the master equation for the scalar field perturbations. We employ metric reconstruction techniques to obtain explicit expressions for all relevant quantities. Finally, by leveraging the properties of spin-weighted spheroidal harmonics to eliminate the angular dependence from the evolution equations, we derive two, radial, second-order, ordinary differential equations for Ψ0 and Ψ4, respectively. These two equations are coupled to another radial, second-order, ordinary differential equation for the scalar field perturbations. This work is the first attempt to derive a master equation for black holes in dynamical Chern-Simons gravity using curvature perturbations. The master equations we obtain can then be numerically integrated to obtain the quasinormal mode spectrum of slowly rotating black holes in this theory, making progress in the study of ringdown in dynamical Chern-Simons gravity. Published by the American Physical Society 2024

Scalar radiation with a quartic Galileon

The class of Galileon scalar fields theories encapsulate the Vainshtein screening mechanism, which is characteristic of a large range of infrared modified theories of gravity. Such theories can lead to testable departures from general relativity through fifth forces and new scalar modes of gravitational radiation. However, the inherent nonlinearity of the Vainshtein mechanism has limited analytic attempts to describe Galileon theories with both cubic and quartic interactions. To improve on this, we perform direct numerical simulations of the quartic Galileon model for a rotating binary source and infer the power spectrum of given multipoles. To tame numerical instabilities we utilize a low-pass filter, extending previous work on the cubic Galileon. Our findings show that the multipole expansion is well defined and under control. Moreover, our results confirm that despite being a nonlinear scalar, the dominant Galileon radiation is quadrupole, and we find a new scaling behavior deep inside the Vainshtein region. Published by the American Physical Society 2024

The average transmitted wave in random particulate materials

Abstract Microwave remote sensing is significantly altered when passing through clouds or dense ice. This phenomenon isn't unique to microwaves; for instance, ultrasound is also disrupted when traversing through heterogeneous tissues. Understanding the average transmission in particle-filled environments is central to improve data extraction or even to create materials that can selectively block or absorb certain wave frequencies. Most methods that calculate the average transmitted field assume that it satisfies a wave equation with a complex effective wavenumber. However, recent theoretical work has predicted more than one effective wave propagating even in a material which is statistically isotropic and for scalar waves. In this work we provide the first clear evidence of these predicted multiple effective waves by using high-fidelity Monte-Carlo simulations that do not make any statistical assumptions. To achieve this, it was necessary to fill in a missing link in the theory for particulate materials: we prove that the incident wave does not propagate within the material, which is usually taken as an assumption called the Ewald-Oseen extinction theorem. By proving this we conclude that the extinction length - the distance it takes for the incident wave to be extinct - is equal to the correlation length between the particles.

Global Models of Collapsing Scalar Field: Endstate

The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analyzed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent horizon formation. Moreover, we examine the stability of initial data in the dynamical system governed by Einstein’s equations, considering variations in parameters that influence naked singularity formation. We illustrate how these results apply to a family of scalar field models, concluding with a discussion on the concept of genericity in singularity studies.

Mode recombination formula and nonanalytic term in an effective potential at finite temperature on a compactified space

We develop a new formula called a mode recombination formula, and we can recast the effective potential at finite temperature in one-loop approximation for fermion and scalar fields on the D-dimensional spacetime, Sτ1×RD−(p+1)×∏i=1pSi1 into a convenient form for discussing nonanalytic terms, which cannot be written in the form of any positive integer power of the field-dependent mass squared, in the effective potential. The formula holds irrespective of whether the field is a fermion or a scalar and of boundary conditions for spatial Si1 directions and clarifies the importance of zero modes in the Matsubara and Kaluza-Klein modes for the existence of the nonanalytic terms. The effective potential is drastically simplified further to obtain the nonanalytic terms in easier and more transparent way. In addition to reproducing previous results, we find that there exists no nonanalytic term for the fermion field with arbitrary boundary condition for the spatial Si1 direction, which is also the case for the scalar field with the antiperiodic boundary condition for the spatial direction. Published by the American Physical Society 2024

Geometric interpretation of Tensor-Vector-Scalar theory in a Kaluza-Klein reference fluid

Abstract Gravitational alternatives to dark matter require additional fields or assumptions beyond general relativity while continuing to agree with tight solar system constraints. Modified Newtonian Dynamics (MOND), for example, predicts the Tully-Fisher relation for galaxies more accurately than dark matter models while limiting to Newtonian gravity in the solar system. On the other hand, MOND does a poor job predicting larger scale observations such as the Cosmic Microwave Background and Matter Power Spectra. Tensor-Vector-Scalar (TeVeS) theory is a relativistic generalization of MOND that accounts for these observations without dark matter. In this paper, I derive a generalized TeVeS from Kaluza-Klein theory in one extra dimension as a consequence of $n=0$ Kaluza-Klein modes. In the KK theory, MOND is a special case of a slicing condition in the 5D ADM formalism enforced by a reference fluid as in the Isham-Kucha\v{r} method which may arise from a broken displacement symmetry. This has two benefits: first is means that TeVeS is compatible with Kaluza-Klein dark matter theory, which is a strong candidate for Weakly Interacting Massive Particles (WIMPs), the other is that it provides an elegant mechanism for the scalar and vector fields. It constrains most of the freedom in the definition of TeVeS which does not have a field theoretic motivation. This is important because the Kaluza-Klein theory predicts that spin-2 tensor modes must propagate at the speed of light, in agreement with observation, from theoretical constraints while TeVeS has to match this observation empirically. Furthermore, it removes need for the interpolating function in MOND and the Lorentz-violating condition on the vector field to be physical since they are analogous to a gauge condition and depend on state of motion.

The two upper critical dimensions of the Ising and Potts models

We derive the exact actions of the Q-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless Q-component scalar field Φα. For the Ising model (Q = 2), the field theory for the spins has upper critical dimension \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{\ ext{c}}}^{{\ ext{spin}}}$$\\end{document} = 4, whereas for the clusters it has \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{\ ext{c}}}^{{\ ext{cluster}}}$$\\end{document} = 6. As a consequence, the probability for three points to be in the same cluster is not given by mean-field theory for d within 4 < d < 6. We estimate the associated universal structure constant as \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C=\\sqrt{6-d}+\\mathcal{O}{\\left(6-d\\right)}^{3/2}$$\\end{document}. This shows that some observables in the Ising model have an upper critical dimension of 4, while others have an upper critical dimension of 6. Combining perturbative results from the ϵ = 6 – d expansion with a non-perturbative treatment close to dimension d = 4 allows us to locate the shape of the critical domain of the Potts model in the whole (Q, d) plane.