Anisotropic Solutions Research Articles

The isotropic attractor solution of axion-SU(2) inflation: universal isotropization in Bianchi type-I geometry

SU(2) gauge fields coupled to an axion field can acquire an isotropic background solution during inflation. We study homogeneous but anisotropic inflationary solutions in the presence of such (massless) gauge fields. A gauge field in the cosmological background may pose a threat to spatial isotropy. We show, however, that such models generally isotropize in Bianchi type-I geometry, and the isotropic solution is the attractor. Restricting the setup by adding an axial symmetry, we revisited the numerical analysis presented in [1]. We find that the reported numerical breakdown in the previous analysis is an artifact of parametrization singularity. We use a new parametrization that is well-defined all over the phase space. We show that the system respects the cosmic no-hair conjecture and the anisotropies always dilute away within a few e-folds.

Gravitational Decoupling in Higher Order Theories

Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this method has also been used to generate exact spherically symmetric solutions of the Einstein-scalar system from the Schwarzschild vacuum metric. This was then used to investigate the effect of scalar fields on the Schwarzschild black hole solution. We show that this method can be extended to higher order theories. In particular, we consider fourth order Einstein–Weyl gravity, and in this case by using the Schwarzschild metric as a seed solution to the associated vacuum field equations, we apply the MGD method to generate a solution to the Einstein–Weyl scalar theory representing a hairy black hole solution. This solution is expressed in terms of a series using the Homotopy Analysis Method (HAM).

Complete deformed charged anisotropic spherical solution satisfying Karmarkar condition

The study of solution for the compact stellar objects such as neutron stars, white dwarfs, and black holes have attracted much consideration in recent days. To discuss this, we extended the charged perfect fluid solution into an anisotropic domain by using the extended gravitational decoupling approach. The charged perfect fluid solution is obtained through the Karmarkar condition by specifying a Finch–Skea spacetime geometry that helps us to determine the decoupling functions. The decoupling function for radial components is determined by using mimic constraint to the seed density while a particular well-behaved function is chosen for the temporal decoupling function. The interior solution is smoothly matched with exterior Reissner–Nordström solution. We found that the obtained charged anisotropic solution is well behaved. In particular, we also studied the impact of gravitational decoupling on pressure, density, mass function, and compactness factor. The detailed physical analysis has been performed via graphical analysis by taking one particular object SMC X-1. Moreover, we have also predicted the radii and compactness factor for 12 compact objects for different values of α. The predicted radii fall between 8 - 15 km.

Anisotropic Strange Star in 5D Einstein-Gauss-Bonnet Gravity.

In this paper, we investigated a new anisotropic solution for the strange star model in the context of Einstein-Gauss-Bonnet (EGB) gravity. For this purpose, we used a linear equation of state (EOS), in particular , (where and are constants) together with a well-behaved ansatz for gravitational potential, corresponding to a radial component of spacetime. In this way, we found the other gravitational potential as well as main thermodynamical variables, such as pressures (both radial and tangential) with energy density. The constant parameters of the anisotropic solution were obtained by matching a well-known Boulware-Deser solution at the boundary. The physical viability of the strange star model was also tested in order to describe the realistic models. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified TOV equation and the dynamical stability through the critical value of the radial adiabatic index. The mass-radius relationship was also established for determining the compactness and surface redshift of the model, which increases with the Gauss-Bonnet coupling constant but does not cross the Buchdahal limit.

Spherically symmetric anisotropic charged solution under complete geometric deformation approach

We present a new systematic approach to find the exact gravitationally decoupled anisotropic spherical solution in the presence of electric charge by using the complete geometric deformation (CGD) methodology. To do this, we apply the transformations over both gravitational potentials by introducing two unknown deformation functions. This new systematic approach allows us to obtain the exact solution of the field equations without imposing any particular ansatz for the deformation functions. Specifically, a well-known mimic approach and equation of state (EOS) have been applied together for solving the system of equations, which determine the radial and temporal deformation functions, respectively. The matching conditions at the boundary of the stellar objects with the exterior Reissner–Nordström metric are discussed in detail. In order to see the physical validity of the solution, we used well-behaved interior seed spacetime geometry and solved the system of equations using the above approaches. Next, we presented several physical properties of the solution through their graphical representations. The stability and dynamical equilibrium of the solution have been also discussed. Finally, we predicted the radii and mass-radius ratio for several compact objects for different decoupling parameters together with the impact of the decoupling parameters on the thermodynamical observables.

Morris–Thorne wormholes in modified f(R, T) gravity

Wormhole solutions obtained by Morris and Thorne (MT) in general relativity (GR) is investigated in a modified theory of gravity. In the gravitational action, we consider f(R, T) which is a function of the Ricci scalar (R) and the trace of the energy-momentum tensor (T). In the framework of a modified gravity described by $$f(R,T)=R+\alpha R^{2}+\lambda T^{\beta }$$ , where $$\alpha $$ , $$\beta $$ and $$\lambda $$ are coupling constants, MT wormhole (WH) solutions with normal matter are obtained for a relevant shape function. We have considered two different values of $$\beta $$ leading to two forms of f(R, T)-gravity. The energy conditions are probed at the throat and away from the throat of the WH. It is found that the coupling parameters, $$\alpha $$ and $$\lambda $$ in the gravitational action play an important role in deciding the matter composition in the wormholes. It is found that for a given $$\lambda $$ , WH exists in the presence of exotic matter at the throat when $$\alpha <0$$ . It is demonstrated here that WH exists even without exotic matter for $$\alpha >0$$ in the modified gravity. Two different shape functions are considered to obtain WH solutions that are permitted with or without exotic matter. It is noted that in a modified f(R, T) gravity MT WH is permitted with normal matter which is not possible in GR. It is demonstrated that a class of WH solutions exist with anisotropic fluid for $$\lambda \ne -8\pi $$ . However, for flat asymptotic regions with anisotropic fluids WH solutions cannot be realized when $$\lambda =-8\pi $$ . All the energy conditions are found consistent with the hybrid shape function indicating existence of WH even with normal matter for $$\lambda \rightarrow 0$$ .

Effects of [formula omitted] gravity on anisotropic charged compact structures

This paper focuses on the analysis of static spherically symmetric anisotropic solutions in the presence of electromagnetic field through the gravitational decoupling approach in f(R,T,RγυTγυ) gravity. We use geometric deformation only on radial metric function and obtain two sets of the field equations. The first set deals with isotropic fluid while the second set yields the influence of anisotropic source. We consider the modified Krori–Barua charged isotropic solution for spherical self-gravitating star to deal with the isotropic system. The second set of the field equations is solved by taking two different constraints. We then investigate physical acceptability of the obtained solutions through graphical analysis of the effective physical variables and energy conditions. We also analyze the effects of charge on different parameters, (i.e., mass, compactness and redshift) for the resulting solutions. It is found that our both solutions are viable as well as stable for specific values of the decoupling parameter φ and charge. We conclude that a self-gravitating star shows more stable behavior in this gravity.

Compact objects by gravitational decoupling in f(R) gravity

The objective of this paper is to discuss anisotropic solutions representing static spherical self-gravitating systems in f(R) theory. We employ the extended gravitational decoupling approach and transform temporal as well as radial metric potentials which decomposes the system of non-linear field equations into two arrays: one set corresponding to seed source and the other one involves additional source terms. The domain of the isotropic solution is extended in the background of f(R) Starobinsky model by employing the metric potentials of Krori–Barua spacetime. We determine two anisotropic solutions by employing some physical constraints on the extra source. The values of unknown constants are computed by matching the interior and exterior spacetimes. We inspect the physical viability, equilibrium and stability of the obtained solutions corresponding to the star Her X-I. It is observed that one of the two extensions satisfies all the necessary physical requirements for particular values of the decoupling parameter.

Tensorial elastodynamics for anisotropic media

Elastic wavefield solutions computed by finite-difference (FD) methods in complex anisotropic media are essential elements of elastic reverse time migration and full-waveform inversion analyses. Cartesian formulations of such solution methods, though, face practical challenges when aiming to represent curved interfaces (including free-surface topography) with rectilinear elements. To forestall such issues, we have developed a general strategy for generating solutions of tensorial elastodynamics for anisotropic media (i.e., tilted transversely isotropic or even lower symmetry) in non-Cartesian computational domains. For the specific problem of handling free-surface topography, we define an unstretched coordinate mapping that transforms an irregular physical domain to a regular computational grid on which FD solutions of the modified equations of elastodynamics are straightforward to calculate. Our fully staggered grid (FSG) with a mimetic FD (MFD) (FSG + MFD) approach solves the velocity-stress formulation of the tensorial elastic wave equation in which we compute the stress-strain constitutive relationship in Cartesian coordinates and then transform the resulting stress tensor to generalized coordinates to solve the equations of motion. The resulting FSG + MFD numerical method has a computational complexity comparable with Cartesian scenarios using a similar FSG + MFD numerical approach. Numerical examples demonstrate that our solution can simulate anisotropic elastodynamic field solutions on irregular geometries; thus, it is a reliable tool for anisotropic elastic modeling, imaging, and inversion applications in generalized computational domains including handling free-surface topography.

Gravitationally decoupled non-static anisotropic spherical solutions

This paper is devoted for the formulation of new anisotropic solutions for non-static spherically symmetric self-gravitating systems through gravitational decoupling technique. Initially, we add a gravitational source in the perfect matter distribution for inducing the effects of anisotropy in the considered model. We then decouple the field equations through minimal geometric deformation approach and derive three new anisotropic solutions. Among these, two anisotropic solutions are evaluated by applying specific constraints on anisotropic source and the third solution is obtained by employing the barotropic equation of state. The physical acceptability and stability of the anisotropic models are investigated through energy conditions and causality condition, respectively. We conclude that all the derived anisotropic solutions are physically viable as well as stable.

Gravitational cracking and complexity in the framework of gravitational decoupling

In this work we analyse the stability of self gravitating spheres in the context of gravitational cracking. Besides exploring the role played by the anisotropy in the occurrence of cracking, we also study the effect of the complexity factor recently introduced by L. Herrera in Phys. Rev. D 97, 044010 (2018). The models under study correspond to anisotropic solutions obtained in the framework of the Gravitational Decoupling. The effect that the variation of the decoupling parameter and the compactness of the source have on the behaviour of the radial force is studied in detail.

Anisotropic charged compact stellar configurations in the perspective of gravitational decoupling approach

We construct the physically admissible charged compact star models threaded with anisotropic matter contents via gravitational decoupling approach. Durgapal IV solution containing charge is considered as seed solution for applying minimal geometric deformation approach. We extend the isotropic seed solution into anisotropic domain by imposing suitable mimic constraints on the physical variables i.e. pressure and density. The extended solution is employed to frame the models of dense relativistic structures. We study the geometrical and thermodynamic behavior of the models and examine the physically admissible attributes of the models via graphical patterns. The stability status of the compact entities is examined through different stability criteria. The essential energy bounds are found to be satisfied within the compact star models. We performed the extensive analysis of the model for the star RXJ 1856-37 having mass 0.9 M Θ and radius 6 km. The extended anisotropic solution is also compatible with observed masses as well as radii of some compact stars EXO 1785-248 and PSR J1614-2230.

Anisotropic power-law inflation for a model of two scalar and two vector fields

Inspired by an interesting counterexample to the cosmic no-hair conjecture found in a supergravity-motivated model recently, we propose a multi-field extension, in which two scalar fields are allowed to non-minimally couple to two vector fields, respectively. This model is shown to admit an exact Bianchi type I power-law solution. Furthermore, stability analysis based on the dynamical system method is performed to show that this anisotropic solution is indeed stable and attractive if both scalar fields are canonical. Nevertheless, if one of the two scalar fields is phantom then the corresponding anisotropic power-law inflation turns unstable as expected.

Piezoresponse in Ferroelectric Materials under Uniform Electric Field of Electrodes.

The analytical solution for the displacements of an anisotropic piezoelectric material in the uniform electric field is presented for practical use in the “global excitation mode” of piezoresponse force microscopy. The solution is given in the Wolfram Mathematica interactive program code, allowing the derivation of the expression of the piezoresponse both in cases of the anisotropic and isotropic elastic properties. The piezoresponse’s angular dependencies are analyzed using model lithium niobate and barium titanate single crystals as examples. The validity of the isotropic approximation is verified in comparison to the fully anisotropic solution. The approach developed in the paper is important for the quantitative measurements of the piezoelectric response in nanomaterials as well as for the development of novel piezoelectric materials for the sensors/actuators applications.

Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions

We elaborate on statistical thermodynamics models of relativistic geometric flows as generalisations of G. Perelman and R. Hamilton theory centred around C. Carath\'{e}odory axiomatic approach to thermodynamics with Pfaffian differential equations. The anholonomic frame deformation method, AFDM, for constructing generic off--diagonal and locally anisotropic cosmological solitonic solutions in the theory of relativistic geometric flows and general relativity is developed. We conclude that such solutions can not be described in terms of the Hawking--Bekenstein thermodynamics for hypersurface, holographic, (anti) de Sitter and similar configurations. The geometric thermodynamic values are defined and computed for nonholonomic Ricci flows, (modified) Einstein equations, and new classes of locally anisotropic cosmological solutions encoding solitonic hierarchies.

A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry

Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain ‘critical’ velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied some time ago. A generalization to anisotropic crystals has been attempted for pure screw and edge dislocations only for some special cases. This work aims to fill the gap of deriving a general anisotropic solution for pure screw dislocations applicable to slip systems featuring a reflection symmetry, a prerequisite to studying pure screw dislocations without mixing with edge dislocations. Further generalizations to arbitrary mixed dislocations as well as regularizations of the dislocation core are beyond the scope of this paper and are left for future work.

Relativistic stellar model in [formula omitted] gravity using karmarkar condition

In the present manuscript, we have constructed an anisotropic solution for spherically symmetric space-time that satisfies Karmarkar’s condition in the context of f(R,T) theory of gravity where R and T represent the Ricci scalar and the trace of Energy-momentum tensor, respectively. In order to achieve our goal, we chose a one of the gravitational potentials having regular behavior and obtained a closed form of the solution. This expression of the gravitational potential enables the embedding equation to be solved and the field equations to be integrated. The resulting current anisotropic solution is well-behaved and can be used to build realistic static fluid spheres. Our anisotropic solution represents compact structures like VelaX−1 and 4U1608−52 to a very high degree of precision. It has also been presented that our stellar model is physically accepted and satisfies all the physical criteria required to meet for a stable hydrostatic equilibrium configuration.

Oriented assembly of monomicelles in beam stream enabling bimodal mesoporous metal oxide nanofibers

The assembly of monomicelles along one-dimension (1D) to construct tubular or fibrous mesostructures is greatly desired but still challenging. Herein, we have demonstrated a facile strategy to synthesize 1D bimodal mesoporous metal oxides (e.g., WO3, WO3/Pd, WO3/PdCu, TiO2, and ZrO2) nanofibers (NFs) through assembling the organic-inorganic composite monomicelles in a beam stream generated via an electrospinning technique. This facile and repeatable methodology relies on the preparation of copolymer@metal-complex monomicelles in an anisotropic solution and oriented assembly of them in the beam stream by the selective evaporation of solvent. WO3 and its derivatives are chosen as the demo, which show a uniform continuous fibrous structure with dual mesopore sizes (∼4.0 and 7.6 nm) and large surface area (∼93.1 m2 g−1). Benefitting from the unique textual structure, gas sensors made by Pd-decorated mesoporous WO3 NFs display outstanding comprehensive sensing performance to ethylbenzene, including a high sensitivity (52.5), an ultralow detection limit (50 ppb), and fast response/recovery kinetics (11/16 s) as well as an outstanding selectivity, which render them promising for rapid environmental monitoring.

EFFECT OF MAGNETIC FIELD ON RHEOLOGICAL PROPERTIES OF CELLULOSE ETHERS SOLUTIONS

The rheological properties, structure and phase transitions of hydroxypropyl cellulose in ethanol, dimethyl sulfoxide, ethylene glycol solutions and ethylcellulose in dimethylformamide solutions are studied using viscometry, the cloud-point method, polarization microscopy, the optical interferometry and a polarization photoelectric apparatus in the temperature range 280-360 K. The temperature-concentration regions of isotropic and anisotropic phases are determined for all systems. The type of boundary curves of phase diagrams is compared with the chemical structure of macromolecules. It is shown that the constant magnetic field (3.6 kOe) leads to the orientation of macromolecules in solutions. The domain structure arising in solutions is fixed after evaporation of a solvent and shown in orientation of strips of the film relief. It was found that the flow curves of all solutions at 298 K in the range of shear rates from 0 to 15 s-1 are typically for the non-Newtonian liquids. It was found that the magnetic field leads to an increase in the viscosity of isotropic solutions and a decrease in the viscosity of anisotropic solutions. Both effects depend on the direction of the magnetic field lines. When the rotor-rotation axis is parallel to the direction of power lines of the magnetic field the change in the viscosity of solutions is greater than that at perpendicular orientation of the rotor-rotation axis and power lines of the magnetic field. The results are discussed using representations about the changes in the macromolecule conformation and in the size and shape of the supramolecular particles in the solutions during flow under a magnetic field with different orientation of the power lines.

Anisotropic spherical solutions via EGD using isotropic Durgapal–Fuloria model

Our main focus is to calculate analytic solutions for spherically symmetric self-gravitating systems using anisotropic fluid via decoupling technique dubbed as extended gravitational decoupling (EGD) approach. To this end, we choose an isotropic Durgapal–Fuloria solution and generalize it to anisotropic domain by transforming temporal and radial metric potentials. We check stability and physical viability of the obtained anisotropic interior solutions via graphical trajectories of energy conditions, TOV equation, causality constraints as well as adiabatic index for the compact stars namely PSR J 1416-2230 and Her X-I. It is found that both of the stellar models exhibit feasible realistic behavior fulfilling all the physical constraints and stability criterion. Hence, the EGD technique is more efficient to explain the interior structure of the stellar objects.