Symmetric Solutions Research Articles

Symmetric Nonradial Solutions for Nonlinear Schrödinger Systems with Mixed Couplings on \(\mathbb R \)\(^{\boldsymbol n}\)

Symmetric Nonradial Solutions for Nonlinear Schrödinger Systems with Mixed Couplings on \(\mathbb R \)\(^{\boldsymbol n}\)

Bifurcation analysis of figure-eight choreography in the three-body problem based on crystallographic point groups

Abstract The bifurcation of figure-eight choreography is analyzed by its symmetry group based on the variational principle of the action. The irreducible representations determine the symmetry and the dimension of the 
Lyapunov-Schmidt reduced action, which yields four types of bifurcations in the sequence of the bifurcation cascade. Type 1 bifurcation, represented by trivial representation, bifurcates two solutions. Type 2, by non-trivial one-dimensional representation, bifurcates two congruent solutions. Type 3 and 4, by two-dimensional irreducible representations, bifurcate two sets of three and six congruent solutions, respectively. We analyze numerical bifurcation solutions previously published and four new ones: 
non-symmetric choreographic solution of type 2, non-planar solution of type 2, y-axis symmetric solution of type 3, and non-symmetric solution of type 4.

On the maximally symmetric vacua of generic Lovelock gravities*

Abstract We survey elementary features of Lovelock gravity and its maximally symmetric vacuum solutions. The latter is solely determined by the real roots of a dimension-dependent polynomial. We also recover the static spherically symmetric (black hole) solutions of Lovelock gravity using Palais’ symmetric criticality principle. We show how to linearize the generic field equations of Lovelock models about a given maximally symmetric vacuum, which turns out to factorize into the product of yet another dimension-dependent polynomial and the linearized Einstein tensor about the relevant background. We also describe how to compute conserved charges using linearized field equations along with the relevant background Killing isometries. We further describe and discuss the special vacua which are defined by the simultaneous vanishing of the aforementioned polynomials.

Analysis on the Propagation and Assembly of Metallic Nanoparticles through Subwavelength Apertures with Overlapping Electrical Double Layers.

Hybrid nanoplasmonic structures composed of subwavelength apertures in metallic films and nanoparticles have recently been demonstrated as ultrasensitive plasmonic sensors. This work investigates the electrokinetically driven propagation of the assembly mechanism of the metallic nanoparticles through nanoapertures. The Debye-Hückel approximation for a symmetric electrolyte solution with overlapping electrical double layers (EDLs) is used to obtain an analytical solution to the problem. The long-term silver nanoparticle concentration response is derived using the homogenization method and a multiscale analysis. The results indicate that uncharged nanoparticles will flow through the nanohole array if the nanochannel height is larger than the Debye length (h 0 > λD), while a trapping mechanism occurs, due to the overlapping of the EDL, when h 0 ∼ 3.8λD. For charged nanoparticles, the response to the electric field occurs locally with the walls of the nanochannel, regardless of its height. For a critical value of the nanochannel length, the leading order of the concentration field becomes purely diffusive.

Revisiting the static spherically symmetric solutions of gravity with a conformally coupled scalar field

Revisiting the static spherically symmetric solutions of gravity with a conformally coupled scalar field

Charged Stellar Structures with Adler-Finch-Skea Geometry in Ricci-inverse Gravity

Abstract We obtain a class of charged, anisotropic, and spherically symmetric solution characterized by the function $f(\mathcal{R},\mathcal{A})=\mathcal{R}+\alpha \mathcal{A}$, where $\mathcal{R}$ is the Ricci scalar, $\mathcal{A}$ is anticurvature scalar, and $\alpha$ is the coupling constant. The model was developed by utilizing the Karmarkar condition to produce the radial metric coefficient and adopting the time metric coefficient as proposed by Adler. We formulated the model by assuming a specific type of charge distribution within the stellar interior. We elaborated boundary conditions to ensure the continuity of the spacetime, considering the exterior spacetime as Bardeen's solution. In addition, we analyzed several physical entities, including the energy density, pressure components, anisotropy in pressure, energy conditions, equation of state, surface redshift, compactness factor, adiabatic index, sound speed, and Tolman-Oppenheimer-Volkoff equilibrium condition. The aforementioned conditions were satisfied, indicating that the solutions derived in this study are within the physically acceptable range.

Complete stability for spherically symmetric backgrounds in beyond Horndeski theory

In this paper, we consider a general static, spherically symmetric background in the quadratic beyond Horndeski theory and analyze the behavior of linear perturbations in both parity odd and parity even sectors. We derive a full set of stability conditions for an arbitrary static, spherically symmetric solution which guarantees absence of ghosts, gradient instabilities, tachyons and superluminal modes in both sectors.

Symmetry-breaking bifurcation for necrotic tumor model with two free boundaries

In this paper, we study a 2-dimensional free boundary problem modeling the tumor growth with a necrotic core. This model has three parameters: σD is a threshold value of nutrient concentration for distinguishing whether tumor cells are alive or not, σ̃ is the death rate of proliferating cells and ν is the removal rate of necrotic cells. With the assumption of σ̃−σD−ν≤0, we first give a complete classification of σD and σ̃ under which the necrotic problem either has the unique radially symmetric stationary solution σs,ps,ρs,Rs or no solutions. Furthermore, we derive the existence of symmetry-breaking solutions bifurcating from the radially symmetric solution σs,ps,ρs,Rs for every γl(l=2,3,…).

Schottky Anomaly of the Kalb-Ramond-de Sitter Spacetime

In the theory of gravity, the spontaneous breaking of Lorentz symmetry due to the non-minimal coupling between the Kalb-Ramond field and Einstein gravity results in the existence of exactly static and spherically symmetric black hole solutions related to the Lorentz violating parameter. Based on the consideration of the interaction between the black hole and cosmological horizons, this paper studies the thermodynamic properties of Kalb-Ramond-de Sitter (KR-dS) spacetime. The Smarr relation expressed by equivalent thermodynamic quantities is found, and it is proved that the equivalent thermodynamic quantities of the KR-dS spacetime satisfy the universal Euler's theorem. It is discovered that the heat capacity of the KR-dS spacetime with respect to the ratio of the two horizons and the variation curve of the heat capacity with effective temperature possess the characteristics of Schottky specific heat. Moreover, the black hole and the cosmological horizon in the equivalent thermodynamic system are regarded as two different energy levels, and the heat capacity of the KR-dS spacetime is discussed using the general form given by the ordinary two-level system. It is found that the heat capacity of KR-dS spacetime described by equivalent thermodynamic quantities not only conforms to the characteristics of Schottky specific heat but also is consistent with the heat capacity of the ordinary two-level system. This result reflects that when the cosmological constant and the charged carried in the KR-dS spacetime remain unchanged, the heat capacity of the system can be represented by a universal two-level system. By comparing the maximum value of the heat capacity curves, the number of microscopic particles between the two horizons can be estimated, which reflects the quantum properties of the KR-dS spacetime. These studies will open a new perspective to probe the thermodynamics of black holes.

Electrostatic Interaction of Dielectric Particles in an Electrolytic Solution

On the basis of the Poisson-Boltzmann equation the electrostatic interaction between two charged dielectric spherical particles in a symmetric electrolyte solution is considered. The interaction forces between particles of the same radius under the condition of uniform charge distribution on their surfaces in the absence of an external field have been calculated by the finite element method. The dependence of the electrostatic repulsion forces between the particles on the magnitude of the particle charges and the dielectric permittivities of the particle materials and the surrounding medium has been analyzed.

On new regular charged black hole solutions: Limiting Curvature Condition, Quasinormal modes and Shadows

We introduce two new static, spherically symmetric regular black hole solutions that can be obtained from non-linear electrodynamics models. For each solution, we investigate the dynamic stability with respect to arbitrary linear fluctuations of the metric and electromagnetic field, and also examine the energy conditions that those black holes satisfy. Moreover, based on those solutions, we present two additional ones that satisfy the Limiting Curvature Condition. Finally, we make a comparison between the two solutions exploring their null geodesics and circular photon orbits.

Application of Kaluza–Klein theory in modelling compact stars: exploring extra dimensions

ABSTRACT A theoretical framework for calculating the mass–radius curve of compact stars in the Kaluza–Klein space–time is introduced, with one additional compact spatial dimension. Static, spherically symmetric solutions are considered, with the equation of state provided by a zero temperature, interacting multidimensional Fermi gas. To model the strong force between baryons, a repulsive potential is introduced, which is linear in the particle number density. The maximal mass of compact stars is calculated for different model parameters, and with a physical parameter choice, it satisfies observational data, meaning that it is possible to model simple, realistic objects within this framework. Based on this comparison, a limiting size for the observational regime of extra dimensions in compact stars is provided, with $r_\mathrm{c} \gtrsim 0.2$ fm.

A strong unique continuation property for weakly coupled elliptic systems

We establish the validity of a strong unique continuation property for weakly coupled elliptic systems, including competitive ones. Our proof exploits the system-structure of the problem and Carleman estimates. Then, we use our unique continuation theorems to show two nonexistence results. The first one states the nonexistence of nontrivial solutions to a weakly coupled elliptic system with a critical nonlinearity and Dirichlet boundary condition on starshaped domains, whereas the second one yields nonexistence of symmetric least energy solutions for a critical system in more general domains.

Black bounces in Cotton gravity

Recently, J. Harada proposed a theory relating gravity to the Cotton tensor, dubbed as “Cotton gravity” (CG). This is an extension of General Relativity such that every solution of the latter turns out to be a solution of the former (but the converse is not true) and, furthermore, it is possible to derive the cosmological constant as an integration constant within it. In this work we investigate CG by coupling it to both non-linear electrodynamics (NLED) and scalar fields. We study static and spherically symmetric solutions implementing a bouncing behaviour in the radial function so as to avoid the development of singularities, inspired by the Simpson–Visser black bounce and the Bardeen model, both interpreted as magnetic monopoles. We identify the NLED Lagrangian density and the scalar field potential generating such solutions, and investigate the corresponding gravitational configurations in terms of horizons, behaviour of the metric functions, and regularity of the Kretchsman curvature scalar. Our analysis extends the class of non-singular geometries found in the literature and paves the ground for further analysis of black holes in CG.

Role of [formula omitted] gravity with class one space-time in constructing new spherically symmetric stellar solutions

This paper aims to investigate the possibility of generating exact solutions for appropriate anisotropic spherically symmetric systems in F(Q,T) gravity where Q and T are non-metricity and the trace of the energy-momentum tensor respectively. These solutions involve embedding a spherically symmetric static metric into a five-dimensional pseudo-Euclidean space. To solve Einstein's field equations and ensure that the solution is free of center singularities, a physically plausible selection of the metric coefficient grr is used. With the help of the Karmarkar condition, we compute the gtt component of the metric tensor using the metric coefficient grr. At the boundary of the compact star, we match interior spacetime with the exterior spacetime to find the values of unknown constants. To make the solution match the measured mass and radius, we have tuned up the solution for compact star PSRJ1614-220. The behavior of the solution has been thoroughly examined for the same star. By examining the necessary physical characteristics, such as energy conditions, causality condition, hydrostatic equilibrium, pressure-density ratio, Herera Cracking criterion, etc., the physical acceptability of the model in the context of F(Q,T) has been investigated. It is observed that the present solution allows viable modeling of stellar objects in F(Q,T) gravity.

Symmetric solutions to symmetric partial difference equations

This paper studies discrete systems defined by linear difference equations on the lattice Z n that are invariant under a finite group of symmetries, and shows that there always exist solutions to such systems that are also invariant under this group of symmetries.

Mechanisms of amphibian arrestin 1 self-association and dynamic distribution in retinal photoreceptors

Visual arrestin 1 (Arr1) is an essential protein for termination of the light response in photoreceptors. While mammalian Arr1s form dimers and tetramers at physiological concentrations in vitro, oligomerization in other vertebrates has not been studied. Here we examine self-association of Arr1 from two amphibian species, Xenopus laevis (xArr1), and Ambystoma tigrinum (salArr1). Sedimentation velocity analytical ultracentrifugation showed that xArr1 and salArr1 oligomerization is limited to dimers. The KD for dimer formation was 53 μM for xArr1 and 44 μM for salArr1, similar to the 69 μM KD for bovine Arr1 (bArr1) dimers. Mutations of orthologous amino acids important for mammalian Arr1 oligomerization had no impact on xArr1 dimerization. Crystallography showed that the fold of xArr1 closely resembles that of bArr1 and crystal structures in different space groups revealed two potential xArr1 dimer forms: a symmetrical dimer with a C-domain interface (CC dimer), resembling the bArr1 solution dimer, and an asymmetric dimer with an N-domain/C-domain interface. Mutagenesis of residues predicted to interact in either of these two dimer forms yielded modest reduction in dimer affinity, suggesting that the dimer interfaces compete or are not unique. Indeed, small-angle X-ray scattering and protein painting data were consistent with a symmetric anti-parallel solution dimer (AP dimer) distinct from the assemblies observed by crystallography. Finally, a computational model evaluating xArr1 binding to compartment-specific partners and partitioning based on heterogeneity of available cytoplasmic spaces shows that Arr1 distribution in dark adapted photoreceptors is largely explained by the excluded volume effect together with tuning by oligomerization.

Frozen stars: Black hole mimickers sourced by a string fluid

The frozen star is a nonsingular, ultracompact object that, to an external observer, looks exactly like a Schwarzschild black hole, but with a different interior geometry and matter composition. The frozen star needs to be sourced by an extremely anisotropic fluid, for which the sum of the radial pressure and energy density is either vanishing or perturbatively small. Here, we show that this matter can be identified with the string fluid resulting from the decay of an unstable D-brane or a brane-antibrane system at the end of open-string tachyon condensation. The string fluid corresponds to flux tubes emanating from the center and ending at the Schwarzschild radius of the star. The effective Lagrangian for this fluid can be recast into a Born-Infeld form. When the fluid Lagrangian is coupled to that of Einstein’s gravity, the static, spherically symmetric solutions of the equations of motion are shown to be the same as those describing the frozen star model. Frozen stars can therefore be viewed as a gravitationally backreacted BIons model or that of gravitationally confined flux tubes. The Born-Infeld Lagrangian provides a complete set of equations that describe the dynamics of the frozen star in a generic state, which is not necessarily static nor spherically symmetric. Our framework therefore should allow a fully dynamical and out-of-equilibrium description of the frozen star model which will be relevant to gravitational waves observations of mergers of astrophysical black holes. Published by the American Physical Society 2024

Global existence of spherically symmetric solutions for isothermal Euler‐Poisson system outside a ball

In this paper, we consider an isothermal Euler‐Poisson system with self‐gravitational force, modeling a compact star such as a strange quark star. We prove that there exists a global entropy solution with spherical symmetry outside a ball, through the fractional Lax‐Friedrichs scheme and the theory of compensated compactness.

The black-hole limits of the spherically symmetric and static relativistic polytrope solutions

The black-hole limits of the spherically symmetric and static relativistic polytrope solutions