Decoupled anisotropic spheres in self-interacting Brans-Dicke gravity

The focus of this paper is to obtain anisotropic spherically symmetric solutions by means of gravitational decoupling in the background of self-interacting Brans-Dicke theory. We introduce minimal geometric deformation in the radial metric component to decouple the field equations into two arrays. The first set, governed by the seed source, is determined through metric functions of isotropic solution (Heintzmann/Tolman VII spacetimes) while the second set is solved by imposing two constraints on the anisotropic source. The unknown constants are evaluated via matching conditions at the stellar boundary. We investigate the effects of massive scalar field as well as decoupling parameter on the physical structure of anisotropic models and check them for viability through energy conditions. It is concluded that the anisotropic solutions obtained through constraint I are well-behaved for selected values of the decoupling parameter. For the second constraint, the extended Heintzmann solution is viable but anisotropic Tolman solution does not comply with dominant energy condition for higher values of the decoupling parameter.     

Gravitational decoupling for hairy black holes in asymptotic AdS spacetimes

In this study, the gravitational decoupling approach via extended geometric deformation is utilized to generate analytical black hole solutions owing to its simplicity and effectiveness. Considering the external fields surrounding Schwarzschild AdS black holes, we derive hairy black hole solutions in asymptotic AdS spacetime, satisfying the strong and dominant energy conditions. Moreover, we find that if the black hole spacetime is a fluid system, the fluid under each of these conditions is anisotropic.     

Effects of charge on gravitational decoupled anisotropic solutions in f(R) gravity

This paper is devoted to studying charged anisotropic static spherically symmetric solutions through gravitationally decoupled minimal geometric deformation technique in f(R) gravity. For this purpose, we first consider the known isotropic Krori–Barua solution for f(R) Starobinsky model in the interior of a charged stellar system and then include the effects of two types of anisotropic solutions. The corresponding field equations are constructed and the unknown constants are obtained from junction conditions. We analyze the physical viability and stability of the resulting solutions through effective energy density, effective radial/tangential pressure, energy conditions, and causality condition. It is found that both solutions satisfy the stability range as well as other physical conditions for specific values of charge as well as model parameter and anisotropic constant. We conclude that the modified theory under the influence of charge yields more stable behavior of the self-gravitating system.     

New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity

In this work, we apply the anholonomic deformation method for constructing new classes of anisotropic cosmological solutions in Einstein gravity and/or generalizations with nonholonomic variables. There are analyzed four types of, in general, inhomogeneous metrics, defined with respect to anholonomic frames and their main geometric properties. Such spacetimes contain as particular cases certain conformal and/or frame transforms of the well known Friedman-Robertson-Walker, Bianchi, Kasner and Gödel universes and define a great variety of cosmological models with generic off-diagonal metrics, local anisotropy and inhomogeneity. It is shown that certain nonholonomic gravitational configurations may mimic de Sitter like inflation scenarios and different anisotropic modifications without satisfying any classical false-vacuum equation of state. Finally, we speculate on perspectives when such off-diagonal solutions can be related to dark energy and dark matter problems in modern cosmology.     

Minimal geometric deformation in asymptotically (A-)dS space-times and the isotropic sector for a polytropic black hole

In the context of the minimal geometric deformation method, in this paper we implement the inverse problem in a black hole scenario. In order to deal with an anisotropic polytropic black hole solution of the Einstein field equations with cosmological constant, the deformation method is slightly extended. After obtaining the isotropic sector and the decoupler for an anisotropic (A-)dS polytropic black hole solution, we emphasize a possible relation between anisotropization/isotropization and the violation of the energy conditions.     

2+1-dimensional gravitational decoupled anisotropic solutions

This paper investigates exact models for spherically symmetric anisotropic matter distribution in 2+1-dimensions via gravitational decoupling approach. For this purpose, we choose known spherical solutions with perfect fluid in the absence as well as the presence of cosmological constant and extend them to anisotropic models by imposing a constraint on matter components. The physical viability and stability of our developed solutions are investigated through graphical analysis of density, radial/tangential pressure, energy conditions, and causality criterion. It is found that both solutions are stable and satisfy all the physical requirements for the feasible choice of the model parameters.     

Gravitational decoupled charged anisotropic solutions in modified Gauss-Bonnet gravity

This paper is devoted to the study of charged anisotropic exact solutions for spherical geometry in the context of modified Gauss-Bonnet gravity using the gravitational decoupling technique. We take Krori-Barua solution in the presence of charge for a spherically symmetric self-gravitating system and extend it to obtain two anisotropic solutions through some constraints. We study the stability as well as the physical viability criterion of the resulting solutions using anisotropy, squared speed of sound parameter and energy bounds. Both models turn out to be physically viable and stable as they fulfill the required energy conditions and stability criterion. We conclude that the stability of both anisotropic solutions increases with a decrease in charge.     

A New Class of Bianchi Type-I Cosmological Models in Scalar-Tensor Theory of Gravitation and Late Time Acceleration

A new class of a spatially homogeneous and anisotropic Bianchi type-I cosmological models of the universe for perfect fluid distribution within the framework of scalar-tensor theory of gravitation proposed by Sáez and Ballester (Phys. Lett. 113:467, 1986) is investigated. To prevail the deterministic solutions we choose the different scale factors which yield time-dependent deceleration parameters (DP) representing models which generate a transition of the universe from the early decelerated phase to the recent accelerating phase. Three different physically viable models of the universe are obtained in which their anisotropic solutions may enter to some isotropic inflationary era. The modified Einstein’s field equations are solved exactly and the models are found to be in good concordance with recent observations. Some physical and geometric properties of the models are also discussed.     

Some Exact Bianchi Type-V Perfect Fluid Cosmological Models with Heat Flow and Decaying Vacuum Energy Density Λ: Expressions for Some Observable Quantities

In this paper we have obtained some new exact solutions of Einstein’s field equations in a spatially homogeneous and anisotropic Bianchi type-V space-time with perfect fluid distribution along with heat-conduction and decaying vacuum energy density Λ by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein’s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The cosmological constant Λ is found to be a decreasing function of time and positive which is corroborated by results from recent supernovae Ia observations. Expressions for look-back time-redshift, neoclassical tests (proper distance d(z)), luminosity distance red-shift and event horizon are derived and their significance are described in detail. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Bianchi cosmologies with anisotropic matter: Locally rotationally symmetric models

The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following. (i) There exist matter models, compatible with the standard energy conditions, such that solutions of Bianchi type IX (closed cosmologies) need not necessarily recollapse; there is an open set of forever expanding solutions. (ii) Generic type IX solutions associated with a matter model like Vlasov matter exhibit oscillatory behavior toward the initial singularity. This behavior differs significantly from that of vacuum/perfect fluid cosmologies; hence “matter matters”. Finally, we indicate that our methods can probably be extended to treat a number of open problems—in particular, the dynamics of Bianchi type VIII and Kantowski-Sachs solutions.     

各向异性介质三维电磁响应模拟的Ho-GEBA算法

本文基于积分方程法研究并建立了一种模拟横向同性介质中任意各向异性异常 体三维电磁响应的高阶广义扩展Born近似(Ho-GEBA)算法. 首先利用逐次迭代技术给出积分方程的广义级数展开解, 为保证其收敛性, 引入一种各向异性条件下满足压缩映射的迭代算子. 然后利用异常体区域分解技术, 并结合扩展Born近似原理, 得到各向异性介质三维电磁响应的Ho-GEBA解. 为提高效率, 计算过程中采用并矢Green函数的解析表达式. 最后通过数值计算实例对比验证了本文算法的有效性. 关键词： 高阶广义扩展Born近似 积分方程 电磁模拟 解析Green函数     

Two-Fluid Dark Energy Models in Bianchi Type-III Universe with Variable Deceleration Parameter

Some new exact solutions of Einstein’s field equations have come forth within the scope of a spatially homogeneous and anisotropic Bianchi type-III space-time filled with barotropic fluid and dark energy by considering a variable deceleration parameter. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. Under the suitable condition, the anisotropic models approach to isotropic scenario. We also find that during the evolution of the universe, the equation of state (EoS) for dark energy ω ^(de), in both cases, tends to ?1 (cosmological constant, ω ^(de)=?1), by displaying various patterns as time increases, which is consistent with recent observations. The cosmic jerk parameter in our derived models are in good agreement with the recent data of astrophysical observations under appropriate condition. It is observed that the universe starts from an asymptotic Einstein static era and reaches to the ΛCDM model. So from recently developed Statefinder parameters, the behaviour of different stages of the universe has been studied. The physical and geometric properties of cosmological models are also discussed.     

Multikink solutions and deformed defects

In this work we consider an application of the deformation procedure that enables us to construct, systematically, scalar field models supporting multikinks. We introduce a new deformation function in order to realize this task. We exemplify the procedure with three different starting models already known in the literature, and the resulting deformed models have rich minima structures which are responsible for the appearance of multikink configurations. We have also considered an application to braneworld scenarios, where we have obtained interesting configurations corresponding to the multikink solutions.     

Adler–Finch–Skea Anisotropic Solution in f ( $$\mathcal{G}$$ ) Gravity

In this paper, we develop anisotropic solution for spherically symmetric self-gravitating stellar object by employing Karmarkar embedding constraint in the framework of f($$\mathcal{G}$$) gravity. For this purpose, we use the mass and radius of three compact star models, i.e., Her X-1, SAX J 1808.4-3658, and 4U 1820-30 as well as smooth matching of spherical interior and Schwarzschild exterior spacetime geometries. The physical consistency and stability of the derived model is examined for these star models. We conclude that the resulting anisotropic model is physically viable as well as stable as it satisfies all the necessary requirements of the compact stellar objects.     

Brane-world stars from minimal geometric deformation, and black holes

Using the effective four-dimensional Einstein field equations, we build analytical models of spherically symmetric stars in the brane-world, in which the external space-time contains both an ADM mass and a tidal charge. In order to determine the interior geometry, we apply the principle of minimal geometric deformation, which allows one to map general relativistic solutions to solutions of the effective four-dimensional brane-world equations. We further restrict our analysis to stars with a radius linearly related to the total general relativistic mass, and obtain a general relation between the latter, the brane-world ADM mass and the tidal charge. In these models, the value of the star’s radius can then be taken to zero smoothly, thus obtaining brane-world black hole metrics with a tidal charge solely determined by the mass of the source and the brane tension. We find configurations which entail a partial screening of the gravitational mass, and general conclusions regarding the minimum mass for semiclassical black holes are also drawn.     

Cosmological analysis of scalar field models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

This paper determines the existence of Noether symmetry in non-minimally coupled f(R, T) gravity admitting minimal coupling with scalar field models. We consider a generalized spacetime which corresponds to different anisotropic and homogeneous universe models. We formulate symmetry generators along with conserved quantities through Noether symmetry technique for direct and indirect curvature–matter coupling. For dust and perfect fluids, we evaluate exact solutions and construct their cosmological analysis through some cosmological parameters. We conclude that decelerated expansion is obtained for the quintessence model with a dust distribution, while a perfect fluid with dominating potential energy over kinetic energy leads to the current cosmic expansion for both phantom as well as quintessence models.     

Anisotropic spheres with Van der Waals-type equation of state

We study static spherically symmetric space-time to describe relativistic compact objects with anisotropic matter distribution and derive two classes of exact models to the Einstein–Maxwell system with a modified Van der Waals equation of state. We motivate a Van der Waals-type equation of state to physically signify a high-density domain of quark matter, and the generated exact solutions are shown to contain several classes of exact models reported previously that correspond to various physical scenarios. Geometrical analysis shows that the physical quantities are well behaved so that these models may be used to describe anisotropic charged compact spheres.     

Fractional Dynamics from Einstein Gravity,General Solutions,and Black Holes

We study the fractional gravity for spacetimes with non-integer fractional derivatives. Our constructions are based on a formalism with the fractional Caputo derivative and integral calculus adapted to nonholonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange–Finsler and Hamilton–Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, ellipsoid gravitational configurations and imbedding of such objects in solitonic backgrounds.