New Branch Of Solutions Research Articles

Spherically symmetric perfect fluid filled universe within the 4 dimensional Einstein–Gauss–Bonnet gravity formalism with vanishing conformal curvature

Conformally flat spacetime geometry is of immense physical importance. In this conext we obtain the most general solutions for 4 dimensional Einstein-Gauss–Bonnet (4D EGB) static spherically symmetric spacetimes. The standard Schwarzschild incompressible fluid sphere is one possible solution, however, new branches of solutions emerge that have cosmological significance. It is intriguing that the geometry of the new model is given by an exactly known spatially directed potential while the remaining potential is given as an integral. It is not necessary to know the explicit form of the temporally directed potential to analyse the physics of the model. However, at least two explicit exact solutions for both potentials are exhibited. Graphical plots are constructed to show that barring a short interval from the centre of the distribution which may be excised and replaced with a well-behaved fluid, all the elementary physical tests are successful. The model considered does not admit a finite radius hence is not applicable to astrophysical compact objects however the pleasing physical characteristics of the fluid suggests applicability to a perfect fluid filled universe. The model satisfies the causality requirement preventing the sound speed from becoming superluminal as well as the Chandrasekar stability criterion demanded of adiabatic fluids. Moreover all the energy conditions are complied with. The analysis effectively rules out the existence of conformally flat stars in 4D EGB gravity aside from the interior Schwarzschild spacetime.

Scalarized non-topological neutron stars in multi-scalar Gauss\u2013Bonnet gravity

In the present paper we construct novel non-topological, spontaneously scalarized neutron stars in multi-scalar Gauss–Bonnet gravity with maximally symmetric target space, and nontrivial map varphi :spacetime rightarrow target space. The theory is characterized by the fact that for some classes of coupling functions the field equations allow solutions with trivial scalar field, which coincide with the general relativistic ones. For a certain range of parameters those solutions lose stability and new branches of solutions with nontrivial scalar field bifurcate from the trivial branch. For a given set of parameters, those branches are characterized by the number of zeros of the scalar field, and they are energetically more favorable than the general relativistic ones.

A simple, efficient and accurate new Lie--group shooting method for solving nonlinear boundary value problems

The present paper provides a new method for numerical solution of nonlinear boundary value problems. This method is a combination of group preserving scheme (GPS) and a shooting--like technique which takes advantage of two powerful methods for solving nonlinear boundary value problems. This method is very effective to search unknown initial conditions. To demonstrate the computational efficiency, the mentioned method is implemented for some nonlinear exactly solvable differential equations including strongly nonlinear Bratu equation, nonlinear reaction--diffusion equation and one singular nonlinear boundary value problem. It is also applied successfully on two nonlinear three--point boundary value problems and a third--order nonlinear boundary value problem which the exact solutions of this problems are unknown. The examples show the power of method to search for unique solution or multiple solutions of nonlinear boundary value problems with high computational speed and high accuracy. In the test problem 5 a new branch of solutions is found which shows the power of the method to search for multiple solutions and indicates that the method is successful in cases where purely analytic methods are not.

Boson and neutron stars with increased density

We discuss boson stars and neutron stars, respectively, in a scalar-tensor gravity model with an explicitly time-dependent real scalar field. While the boson stars in our model – in contrast to the neutron stars – do not possess a hard core, we find that the qualitative effects of the formation of scalar hair are similar in both cases: the presence of the gravity scalar allows both type of stars to exist for larger central density as well as larger mass at given radius than their General Relativity counterparts. In particular, we find new types of neutron stars with scalar hair which have radii very close to the corresponding Schwarzschild radius and hence are comparable in density to black holes. This new branch of solutions is stable with respect to the decay into individual baryons.

Delamination of open cylindrical shells from soft and adhesive Winkler's foundation.

The interaction between thin elastic films and soft-adhesive foundations has recently gained interest due to technological applications that require control over such objects. Motivated by these applications we investigate the equilibrium configuration of an open cylindrical shell with natural curvature κ and bending modulus B that is adhered to soft and adhesive foundation with stiffness K. We derive an analytical model that predicts the delamination criterion, i.e., the critical natural curvature, κ_{cr}, at which delamination first occurs, and the ultimate shape of the shell. While in the case of a rigid foundation, K→∞, our model recovers the known two-states solution at which the shell either remains completely attached to the substrate or completely detaches from it, on a soft foundation our model predicts the emergence of a new branch of solutions. This branch corresponds to partially adhered shells, where the contact zone between the shell and the substrate is finite and scales as ℓ_{w}∼(B/K)^{1/4}. In addition, we find that the criterion for delamination depends on the total length of the shell along the curved direction, L. While relatively short shells, L∼ℓ_{w}, transform continuously between adhered and delaminated solutions, long shells, L≫ℓ_{w}, transform discontinuously. Notably, our work provides insights into the detachment phenomena of thin elastic sheets from soft and adhesive foundations.

Q-balls in the U(1) gauged Friedberg-Lee-Sirlin model

We consider the U(1) gauged two-component Friedberg-Lee-Sirlin model in 3+1 dimensional Minkowski spacetime, which supports non-topological soliton configurations. Here we found families of axially-symmetric spinning gauged Q-balls, which possess both electric and magnetic fields. The coupling to the gauge sector gives rise to a new branch of solutions, which represent the soliton configuration coupled to a circular magnetic flux. Further, in superconducting phase this branch is linked to vorton type solutions which represent a vortex encircling the soliton. We discuss properties of these solutions and investigate their domains of existence.

Electric double layer of electrons: Attraction between two like-charged surfaces induced by Fermi–Dirac statistics

Recently we reported that Fermi–Dirac statistics of electrons contained between two oppositely charged surfaces separated by the order of nanometers create overlapping electric double layers with repulsive total force between the surfaces. Here, we present a new branch of solutions to the same variational problem resulting in higher energy densities and identify regions of the phase space where the force between two like-charged surfaces is attractive.

Solitons and black hole in shift symmetric scalar-tensor gravity with cosmological constant

We demonstrate the existence of static, spherically symmetric globally regular, i.e. solitonic solutions of a shift-symmetric scalar-tensor gravity model with negative cosmological constant. The norm of the Noether current associated to the shift symmetry is finite in the full space-time. We also discuss the corresponding black hole solutions and demonstrate that the interplay between the scalar-tensor coupling and the cosmological constant leads to the existence of new branches of solutions. To linear order in the scalartensor coupling, the asymptotic space-time corresponds to an Anti-de Sitter space-time with a non-trivial scalar field on its conformal boundary. This allows the interpretation of our solutions in the context of the AdS/CFT correspondence. Finally, we demonstrate that — for physically relevant, small values of the scalar-tensor coupling — solutions with positive cosmological constant do not exist in our model.

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories.

In the present Letter, we consider a class of extended scalar-tensor-Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is excited only in the extreme curvature regime. We show that in the mentioned class of ESTGB theories there exist new black-hole solutions that are formed by spontaneous scalarization of the Schwarzschild black holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and a new branch of solutions with a nontrivial scalar field bifurcates from the Schwarzschild one. As a matter of fact, more than one branch with a nontrivial scalar field can bifurcate at different masses, but only the first one is supposed to be stable. This effect is quite similar to the spontaneous scalarization of neutron stars. In contrast to the standard spontaneous scalarization of neutron stars, which is induced by the presence of matter, in our case, the scalarization is induced by the curvature of the spacetime.

Ineffective higher derivative black hole hair

Inspired by possibility that the Schwarzschild black hole may not be the unique spherically symmetric vacuum solution to generalisations of general relativity, we consider black holes in pure fourth order higher derivative gravity treated as an effective theory. Such solutions may be of interest in addressing the issue of higher derivative hair or during the later stages of black hole evaporation. Non-Schwarzschild solutions have been studied but we have put earlier results on a firmer footing by finding a systematic asymptotic expansion for the black holes and matching them with known numerical solutions obtained by integrating out from the near horizon region. These asymptotic expansions can be cast in the form of trans-series expansions which we conjecture will be a generic feature of non-Schwarzschild higher derivative black holes. Excitingly we find a new branch of solutions with lower free energy than the Schwarzschild solution, but as found in earlier work, solutions only seem to exist for black holes with large curvatures meaning that one should not generically neglect even higher derivative corrections. This suggests that one effectively recovers the non-hair theorems in this context.

The Mimetic Born-Infeld Gravity: The Primordial Cosmos and Spherically Symmetric Solutions

The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions. We study a realistic primordial vacuum universe and we prove the existence of regular solutions. Besides, the linear instabilities in the EiBI model are found to be avoidable for some bouncing solutions. For a vacuum, static and spherically symmetric geometry, a new branch of solutions in which the black hole singularity that is replaced with a lightlike singularity is found.

Surfing the edge: using feedback control to find nonlinear solutions

Many transitional wall-bounded shear flows are characterised by the coexistence in state space of laminar and turbulent regimes. Probing the edge boundary between the two attractors has led in the last decade to the numerical discovery of new (unstable) solutions to the incompressible Navier–Stokes equations. However, the iterative bisection method used to compute edge states can become prohibitively costly for large systems. Here we suggest a simple feedback control strategy to stabilise edge states, hence accelerating their numerical identification by several orders of magnitude. The method is illustrated for several configurations of cylindrical pipe flow. Travelling waves solutions are identified as edge states, and can be isolated rapidly in only one short numerical run. A new branch of solutions is also identified. When the edge state is a periodic orbit or chaotic state, the feedback control does not converge precisely to solutions of the uncontrolled system, but nevertheless brings the dynamics very close to the original edge manifold in a single run. We discuss the opportunities offered by the speed and simplicity of this new method to probe the structure of both state space and parameter space.

On asymmetric generalized solitary gravity-capillary waves in finite depth.

Generalized solitary waves propagating at the surface of a fluid of finite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. Both the effects of gravity and surface tension are included. It is shown that in addition to the classical symmetric waves, there are new asymmetric solutions. These new branches of solutions bifurcate from the branches of symmetric waves. The detailed bifurcation diagrams as well as typical wave profiles are presented.

Rheology of micropolar fluid in a channel with changing walls: Investigation of multiple solutions

A numerical study is carried out in order to investigate the multiple solutions of micropolar fluid in a channel with changing walls. Mathematical modeling of laws of conservation of mass, momentum, angular momentum and energy is performed and governing partial differential equations are converted into self-similar ordinary differential equations by applying suitable similarity transformation and then solved numerically by shooting method. A new branch of solutions is found and presented graphically and numerically for the various values of parameters, which has never been reported.

Strong-field dynamo action in rapidly rotating convection with no inertia.

The earth's magnetic field is generated by dynamo action driven by convection in the outer core. For numerical reasons, inertial and viscous forces play an important role in geodynamo models; however, the primary dynamical balance in the earth's core is believed to be between buoyancy, Coriolis, and magnetic forces. The hope has been that by setting the Ekman number to be as small as computationally feasible, an asymptotic regime would be reached in which the correct force balance is achieved. However, recent analyses of geodynamo models suggest that the desired balance has still not yet been attained. Here we adopt a complementary approach consisting of a model of rapidly rotating convection in which inertial forces are neglected from the outset. Within this framework we are able to construct a branch of solutions in which the dynamo generates a strong magnetic field that satisfies the expected force balance. The resulting strongly magnetized convection is dramatically different from the corresponding solutions in which the field is weak.

A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems

In this work an iterative method is proposed to predict and demonstrate the existence and multiplicity of solutions for nonlinear boundary value problems. In addition, the proposed method is capable of calculating analytical approximations for all branches of solutions. This method is a combination of reproducing kernel Hilbert space method and a shooting-like technique which takes advantage of two powerful methods for solving nonlinear boundary value problems. The formulation and implementation of this iterative method is discussed for nonlinear second order with two and three-point boundary value problems. Also, the convergence of the proposed method is proved. To demonstrate the computational efficiency, the mentioned method is implemented for some nonlinear exactly solvable differential equations including strongly nonlinear Bratu equation and nonlinear reaction–diffusion equation. It is also applied successfully to two nonlinear three-point boundary value problems with unknown exact solutions. In the last example a new branch of solutions is found which shows the power of the method to search for multiple solutions and indicates that the method may be successful in cases where purely analytic methods are not.

All the solutions of the form M2 × WΣd − 2 for Lovelock gravity in vacuum in the Chern-Simons case

In this paper we classify a certain family of solutions of Lovelock gravity in the Chern-Simons (CS) case, in arbitrary (odd) dimension, d ⩾ 5. The spacetime is characterized by admitting a metric that is a warped product of a two-dimensional spacetime M2 and an (a priori) arbitrary Euclidean manifold Σd−2 of dimension d − 2. We show that the solutions are naturally classified in terms of the equations that restrict Σd−2. According to the strength of such constraints we found the following branches in which Σd−2 has to fulfill: a Lovelock equation with a single vacuum (Euclidean Lovelock Chern-Simons in dimension d − 2), a single scalar equation that is the trace of an Euclidean Lovelock CS equation in dimension d − 2, or finally a degenerate case in which Σd−2 is not restricted at all. We show that all the cases have some degeneracy in the sense that the metric functions are not completely fixed by the field equations. This result extends the static five-dimensional case previously discussed in Dotti et al. [Phys. Rev. D 76, 064038 (2007)]10.1103/PhysRevD.76.064038, and it shows that in the CS case, the inclusion of higher powers in the curvature does not introduce new branches of solutions in Lovelock gravity. Finally, we comment on how the inclusion of a non-vanishing torsion may modify this analysis.

General relativity limit of Hořava-Lifshitz gravity with a scalar field in gradient expansion

We present a fully nonlinear study of long wavelength cosmological perturbations within the framework of the projectable Horava-Lifshitz gravity, coupled to a single scalar field. Adopting the gradient expansion technique, we explicitly integrate the dynamical equations up to any order of the expansion, then restrict the integration constants by imposing the momentum constraint. While the gradient expansion relies on the long wavelength approximation, amplitudes of perturbations do not have to be small. When the $\lambda\to 1$ limit is taken, the obtained nonlinear solutions exhibit a continuous behavior at any order of the gradient expansion, recovering general relativity in the presence of a scalar field and the "dark matter as an integration constant". This is in sharp contrast to the results in the literature based on the "standard" (and naive) perturbative approach where in the same limit, the perturbative expansion of the action breaks down and the scalar graviton mode appears to be strongly coupled. We carry out a detailed analysis on the source of these apparent pathologies and determine that they originate from an improper application of the perturbative approximation in the momentum constraint. We also show that there is a new branch of solutions, valid in the regime where $|\lambda-1|$ is smaller than the order of perturbations. In the limit $\lambda\to1$, this new branch allows the theory to be continuously connected to general relativity (plus "dark matter").

Parameter-dependent systems on the half-line and free convection boundary-layers in porous media

In this paper we use a recently elaborated abstract method, for parameter-dependent ODE systems over the interval (0, ∞), to obtain existence results for the problem of self-similar solutions in boundary-layer free convection in porous media. Using a generalization of the method to exponentially decaying solutions, we are able to recover some known results, and to obtain a new branch of solutions in the case of the so-called backward boundary-layer. The arguments involve the derivation of suitable a priori estimates for the solutions of the problem.

Bifurcations from regular quotient networks: A first insight

We consider regular (identical-edge identical-node) networks whose cells can be grouped into classes by an equivalence relation. The identification of cells in the same class determines a new network — the quotient network. In terms of the dynamics, this corresponds to restricting the coupled cell systems associated with a network to flow-invariant subspaces given by equality of certain cell coordinates. Assuming a bifurcation occurs for a coupled cell system restricted to the quotient network, we ask how that bifurcation lifts to the overall space. Surprisingly, for certain networks, new branches of solutions occur besides the ones that occur in the quotient network. To investigate this phenomenon we develop a systematic method that enumerates all networks with a given quotient. We also prove necessary conditions for the existence of solution branches not predicted by the quotient. We then apply our method to two particular quotient networks; namely, two- and three-cell bidirectional rings. We show there are no additional bifurcating solution branches when the quotient network is a two-cell bidirectional ring. However, two of the 12 five-cell networks that have the three-cell bidirectional ring as a quotient network exhibit bifurcating solutions that do not occur in the quotient itself. Thus, network architecture sometimes forces the existence of bifurcating branches in addition to the ones determined by the quotient.