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In this manuscript, we have continued the work of Herrera et al. (Gen. Relativ. Gravit. 44, 1143, 2012) to investigate the instability of non-static spheres supported by anisotropic matter configuration in the background of D-dimensional Einstein gravity. For this purpose, we assume that our relativistic sphere undergoes adiabatic evolution with a vanishing expansion scalar condition. We compute gravitational field equations, conservation equations, and junction conditions in D-dimensional Einstein theory. After considering the evolution of the systems under an expansion-free background, some significant constraints are established by using a perturbation scheme. This leads us to develop the dynamical instability of expansion-free anisotropic fluid spheres in the Newtonian (N) and Post-Newtonian (PN) domains. After focusing on the N and PN eras, our study reveals that the adiabatic index (Γ ), does not contribute to the instability ranges in these domains. Instead, these ranges are being determined solely by the anisotropy of fluid pressure, D-dimensional Einstein gravity parameter, and the radial energy density profile. [ABSTRACT FROM AUTHOR]

The present investigation examines the behaviour of compact relativistic objects characterised by static and spherically symmetric space–time for neutral anisotropic matter distribution. More specifically, we consider an equation of state (EoS), in which density and radial pressure are connected with each other quadratically. By smoothly matching the interior space–time with the exterior at the stellar surface, the appropriate values of the constant parameters for physically realistic solutions are obtained to model various compact stars. We explore the physical behaviour of compact stellar models SMC X-4, Vela X-1, CEN X-3, PSR J1614-2230, LMC X-4 and EXO 1785-248. Further, we describe several features of the compact stellar systems that exhibit physically acceptable attributes with no singularity. All important stability criteria, such as the energy conditions, causality conditions, Buchdhal condition and the adiabatic index are fulfilled by our neutral anisotropic compact star models. An in-depth comprehension of the physical characteristics of the proposed solution has been achieved through meticulous analytical and graphical examinations. By utilising this solution, the masses and radii of six compact stellar candidates mentioned above are optimised with the observed values obtained experimentally. The derived solution might be useful to enhance the understanding of the strong-field regimes and self-gravitating entities. [ABSTRACT FROM AUTHOR]

In this paper, we study quintessence compact stars in the paradigm of pure Lovelock gravity. We derive the field equations using a spherically symmetric space–time. Specifically, we discuss the equivalence of Einstein's Lovelock gravity in four-dimensional space–time, Gauss–Bonnet term equivalent Lovelock gravity in seven-dimensional space–time and sixteen-dimensional Lovelock gravity by exploring the impact of the quintessence field parameter on features of compact stars in anisotropic matter fields. For matter inside the star, we use Tolman–Kuchowiz space–time. We discuss the density of the compact star and the density related to the quintessence matter field. We also explore the pressure profiles, anisotropy, speeds of sound for stability, EoS state parameters, mass-to-radius profile, compactification, gravitational and gradients for different values of N, which change the dimensions ( d = 3 N + 1 ) of pure Lovelock gravity. [ABSTRACT FROM AUTHOR]

The aim of this study is to discuss viable anisotropic solutions of self-gravitating system through a minimal geometric deformation approach in the perspective of f (R , T 2) gravity. In this regard, we assume two sources (seed and additional) for the static sphere. The seed source is considered to be isotropic, while the additional source induces anisotropy. The field equations are decoupled into two sets by deforming the radial metric function. The metric potentials of the Krori–Barua solution are employed to obtain exact solution of the field equations while three different constraints are used to find the solutions corresponding to the anisotropic source. Junction conditions are utilised to determine the values of unknown constants at the hypersurface. Finally, we check the viability and stability of the obtained solutions using the star candidate PSR J1614-2230. We show that all the three solutions satisfy the viability conditions. It is found that solution I is stable using both Herrara's cracking as well as squared sound speed approach while solutions II and III are stable using only Herrara's cracking approach. [ABSTRACT FROM AUTHOR]

In this article, we have obtained a gravitationally decoupled Class-I anisotropic solution for compact stars using the Buchdahl-type space–time geometry. The anisotropic solution is obtained by solving Einstein's field equations via a complete geometric deformation (CGD) approach. This CGD approach transforms both gravitational potentials by introducing two unknown functions that govern the equations of motion for extra sources. The solutions for these deformation functions are derived using mimic constraint to density and equation of state (EoS) between extra source components rather than imposing a particular ansatz for them. To ensure that the solution describes a physically realisable stellar structure, we have tested the physical viability of the solution based on its regularity and stability conditions. We observed that the decoupling parameter suppresses the pressure, energy density and mass of the stellar objects. Also, the radii for several known astrophysical objects have been predicted for different values of the decoupling constant. The obtained results show that gravitational decoupling yields more compact objects than pure Einstein's GR. [ABSTRACT FROM AUTHOR]

Exact solutions to Einstein–Maxwell systems play an important role in relativistic astrophysics. In this paper, a new technique to generate exact solutions to the Einstein–Maxwell system is proposed. Corresponding to a spherically symmetric charged fluid sphere, by specifying the electric field and for a particular form of the metric potential g rr , a new solution is obtained in terms of hypergeometric functions. Subsequently, for specific choice of model parameters, many closed-form solutions are developed. In the process, it is possible to regain a number of well-known stellar models which had been developed earlier with or without the presence of charge following the Vaidya and Tikekar ansatz for compact stars (J. Astrophys. Astron. 3:325 (1982); J. Math. Phys.31:2454 (1990)). It is shown that the new class of solutions can be used as viable models for compact stars for a wide range of values of the model parameters. Physical behaviour of the resultant stellar configurations are studied. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic delayed HIV/AIDS model involving humans with immunity is formulated. We study the dynamics of the mathematical model of HIV/AIDS epidemic with discrete and distributed delays. The basic reproduction number R 0 d of the deterministic model and R 0 s of the corresponding stochastic model are identified. Using appropriate Lyapunov functionals, we obtain sufficient conditions for the extinction of the disease by studying the dynamics of the disease-free equilibrium E 0 . We show the regions of stability of E 0 and some computer simulations are carried out to present the effect of the stochastic environmental noise and the delay tactics. Sensitivity of R 0 s with respect to the noise parameter σ and the delay τ is shown. Our study shows that the increase in the delay tactics and the noise help in the possible extinction, as needed. [ABSTRACT FROM AUTHOR]

In this paper, the quasi static-approximation on the hydrodynamics of compact objects is proposed in f(R, T) gravity, where R is the scalar curvature and T is the trace of stress-energy tensor, by exploring the axial and reflection symmetric spacetime stuffed with anisotropic and dissipative matter contents. The set of invariant-velocities is defined to comprehend the concept of quasi static-approximation. As a consequence, the evolution of compact objects is shown by analyzing the corresponding modified field, dynamical and scalar equations in this approximation to evoke all the feasible outcomes. Furthermore, the significance of kinematical quantities, modified heat-fluxes and scalar variables are found through the proposed approximation. [ABSTRACT FROM AUTHOR]

We present an anisotropic charged analogue of Kuchowicz (1971) solution of the general relativistic field equations in curvature coordinates by using simple form of electric intensity E and pressure anisotropy factor Δ that involve charge parameter K and anisotropy parameter α , respectively. Our solution is well behaved in all respects for all values of X (X is related to the radius of the star) lying in the range 0 < X ≤ 0.6 , α lying in the range 0 ≤ α ≤ 1.3 , K lying in the range 0 < K ≤ 1.75 and Schwarzschild compactness parameter "u" lying in the range 0 < u ≤ 0.338 . Since our solution is well behaved for a wide range of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We present some models of super-dense quark stars and neutron stars corresponding to X = 0.2 , α = 0.2 and K = 0.5 for which u max = 0.15 . By assuming surface density ρ b = 4.6888 × 10 14 g / c c , the mass and radius are 0.955 M ⊙ and 9.439km, respectively. For ρ b = 2.7 × 10 14 g / c c , the mass and radius are 1.259 M ⊙ and 12.439km, respectively, and for ρ b = 2 × 10 14 g / c c , the mass and radius are 1.463 M ⊙ and 14.453km, respectively. It is also shown that inclusion of more electric charge and anisotropy enhances the static stable configuration under radial perturbations. The M - R graph suggests that the maximum mass of the configuration depends on the surface density, i.e., with the increase in surface density, the maximum mass and corresponding radius decrease. This may be because of existence of exotic matters at higher densities that soften the EoSs. [ABSTRACT FROM AUTHOR]

In this paper, we explore the physical aspects that create complexity within a static anisotropic cylindrical source in the framework of self-interacting Brans–Dicke theory. We split the Riemann tensor to formulate structure scalars associated with fundamental properties of the fluid in the presence of the scalar field. We define the complexity factor based on these scalars and then discuss the criteria for zero complexity. Finally, we use the condition of vanishing complexity as a constraint to check the behavior for two compact objects. It is deduced that the inclusion of the scalar field increases the complexity of the system. [ABSTRACT FROM AUTHOR]

In this paper, we present the bulk viscous phenomena to mimic new holographic dark energy behavior in modified f(R, T) gravity. We assume the bulk viscosity coefficient, ζ in the form of ζ = ζ 0 + ζ 1 H , where ζ 0 , ζ 1 are positive constants and H is the Hubble parameter. We obtain the exact solution of the scale factor and classify all the possible scenarios (deceleration, acceleration and their transition) of the evolution of the Universe. It is observed that the model transits from the decelerated phase to accelerated phase in early or late time depending on the values of viscous terms. For large values of viscous terms, the model always accelerates throughout the evolution. Furthermore, we also analyze two diagnostic parameters, statefinder r , s and Om to discriminate our model with the other existing dark energy models. The evolutions of these diagnostics are shown in r - s , r - q and Om − z planes. It is found that the behavior of trajectories in different planes depends on the bulk viscous coefficients. A small combination of ζ 0 and ζ 1 gives the quintessence-like behavior, whereas a large combination gives Chaplygin gas-like model. However, the model approaches the ΛCDM model in the late time evolution of the Universe. The value of the effective equation of state parameter comes to be − 0.9745 which is very close to the observational data. The entropy and generalized second law of thermodynamics are valid under certain constraints. The analysis shows that the dark energy phenomena may be explained in the presence of bulk viscosity in the modified theory of gravity. [ABSTRACT FROM AUTHOR]

In many circumstances the perfect fluid conservation equations can be directly integrated to give a geometric-thermodynamic equation: typically that the lapse N is the reciprocal of the enthalphy h, (N = 1/h). This result is aesthetically appealing as it depends only on the fluid conservation equations and does not depend on specific field equations such as Einstein's. Here the form of the geometric-thermodynamic equation is derived subject to spherical symmetry and also for the shift-free ADM formalism. There at least three applications of the geometric-thermodynamic equation, the most important being to the notion of asymptotic flatness and hence to spacetime exterior to a star. For asymptotic flatness one wants h → 0 and N → 1 simultaneously, but this is incompatible with the geometric-thermodynamic equation. Observational data and asymptotic flatness are discussed. It is argued that a version of Mach's principle does not allow asymptotic flatness.

The paper deals with the dynamical evolution of a homogeneous and anisotropic Bianchi V model filled with perfect fluid and scalar field. The two sources are assumed to be non-interacting. The average scale factor and scalar potential are assumed to be the exponential functions of the scalar field. After constructing the scenario, the exact solutions of the field equations are obtained. We use the observational data in order to find the parameters $$\alpha$$ and β, used in average scale factor and scalar potential, respectively. The roles of scalar field through the variable equation of state (EoS) parameters are studied in detail. We observe that during the evolution of the Universe the EoS parameters change from phantom region to quintessence region for some small values of $$\alpha$$ and β, respectively. This implies that the model shows phantom behaviour during early time and quintessence in late time evolution. However, for the large values of $$\alpha$$ and β these EoS parameters vary in quintessence region only in both cases. We also find the statefinder parameters which shows that the model behaves like $$\Lambda$$ CDM or SCDM depending on the constant values of $$\alpha$$ and β. [ABSTRACT FROM AUTHOR]

In present article we extend one of our earlier works Bhar et al. (Astrophys. Space Sci. 359: 13, 2015) by considering quadratic equation of state for the matter distribution. The solution has its distinct feature as the EoS chosen is quadratic and is presenting for the first time in Tolman VII background. The solution is well behaved in nature in all respects and satisfies energy conditions. The solution is also free from central singularities and satisfies Buchdahl condition. Using this solution, we optimized the masses and radii of few well-known compact stars namely Her X-1, RX J1856.5-3754, PSR B0943 + 10, PSR B1913 + 16 and Cyg X-2 with their experimentally observed values. [ABSTRACT FROM AUTHOR]

We present charged anisotropic Durgapal IV interior solutions of the general relativistic field equations in curvature coordinates. These exact solutions can be used to model stable and well-behaved compact stars. Using these solutions we have presented models of well-known neutron and quark stars such as PSR J1903+0327, RX-J1856.5-3754, PSR B1913+16, PSR J0737-3039A and Cyg X-2. The equation of state (EoS) corresponding to the modeled objects are studied using their compression moduli. According to our solutions it is found that the EoS for Cyg X-2 (neutron star) is stiffer than any other object presented and therefore more massive. Furthermore, the EoS for RX J1856.5-3754 (Quark star) is the softest one, rendering it least massive. These solutions satisfy all the energy conditions. Finally, all our presented stellar models satisfy the equilibrium condition of Cooperstock and de la Cruz i.e. M > Q . [ABSTRACT FROM AUTHOR]

In this paper, we present generalization of anisotropic analogue of charged Heintzmann's solution of the general relativistic field equations in curvature coordinates. These exact solutions are stable and well behaved in all respect for a wide range of anisotropy parameter and charge parameter. We have found that these new solutions are suitable for the modeling of super dense stars like neutron stars and quark stars because they yield a wide range of masses and radii with simple mathematical expressions. By tuning different values of the few parameters, we can model various neutron stars and quark stars which are compatible with the experimentally observed values of masses and radii. Therefore, we have synchronized our solution with the observed values of some of the compact stars XTE J1739 − 217, EXO 0748 − 676, PSR J1614 − 2230, PSR J0348 + 0432 and PSR B0943 + 10. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the stability of cylindrical thin-shell wormholes. We follow the Visser's cut and paste approach for the construction of thin-shell. The Darmois-Israel formalism is used to determine the stress-energy tensor. The null and weak energy conditions as well as attractive and repulsive characteristics of thin-shell wormholes are analyzed. We find both stable and unstable solutions by taking dark energy, generalized cosmic Chaplygin gas, and modified cosmic Chaplygin gas models as exotic matter at the wormhole throat. Finally, we compare our results with those for modified generalized Chaplygin gas model. [ABSTRACT FROM AUTHOR]

The Kramer radiating star uses the interior Schwarzschild solution as a seed solution to generate a model of dissipative collapse. We investigate the thermal behaviour of the radiating star by employing a causal heat transport equation. The causal temperature is explicitly determined for the first time by integrating the transport equation. We further show that the dissipation of energy to the exterior space-time renders the core more unstable than the cooler surface layers. [ABSTRACT FROM AUTHOR]

We study under what conditions the thermal peeling is present for dissipative local and quasi-local anisotropic spherical matter configurations. Thermal peeling occurs when different signs in the velocity of fluid elements appear, giving rise to the splitting of the matter configuration. The evolution is considered in the quasi-static approximation and the matter contents are radiant, anisotropic (unequal stresses) spherical local, and quasi-local fluids. The heat flux and the associated temperature profiles are described by causal thermodynamics consistent with this approximation. It is found that both types of configurations can exhibit thermal peeling when most of the radiated energy emerges from the first half of the distribution, and thermal peeling appears to be associated with extreme astrophysical scenarios (highly relativistic and very energetic gravitational system). [ABSTRACT FROM AUTHOR]

We present the plausibility of some models emerging from an algorithm devised to generate a one-parameter family of interior solutions for the Einstein equations. We explore how their physical variables change as the family parameter varies. The models studied correspond to anisotropic spherical matter configurations having a nonlocal equation of state. This particular type of equation of state, with no causality problems, provides at a given point the radial pressure not only as a function of the density but as a functional of the enclosed matter distribution. We have found that there are several model-independent tendencies as the parameter increases: the equation of state tends to be stiffer and the total mass becomes half of its external radius. Profiting from the concept of cracking of materials in general relativity, we obtain that these models become more potentially stable as the family parameter increases. [ABSTRACT FROM AUTHOR]

In this paper, we investigate exact solutions of the field equations for charged, anisotropic, static, cylindrically symmetric space-time. We use a barotropic equation of state linearly relating the radial pressure and energy density. The analysis of the matter variables indicates a physically reasonable matter distribution. In the most general case, the central densities correspond to realistic stellar objects in the presence of anisotropy and charge. Finally, we conclude that matter sources are less affected by the electromagnetic field. [ABSTRACT FROM AUTHOR]

A sine-Gordon soliton star model with a mix of dark energy and Fermi matter is studied in the two-dimensional Brans-Dicke gravity model. The phase structure is analysed for a strong-coupling Thirring model. Subsequently, a soliton star model with cool Fermi matter coupling is constructed. We found that the soliton state and the mass of a star can change the density and pressure of matter at certain temperatures. Moreover, the stability of dark energy in the center of a star is proved when the coupling coefficient of the scalar field and Fermi matter satisfies some constraint conditions. [ABSTRACT FROM AUTHOR]

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This paper investigates cylindrically symmetric distribution of an anisotropic fluid under the expansion-free condition, which requires the existence of a vacuum cavity within the fluid distribution. We have discussed two families of solutions that further provide two exact models in each family. Some of these solutions satisfy the Darmois junction condition while some show the presence of a thin shell on both boundary surfaces. We also formulate a relation between the Weyl tensor and energy density. [ABSTRACT FROM AUTHOR]

In this study, we consider a charged anisotropic fluid cylinder with no external pressure acting on the fluid. This is a cylindrical version of Krori and Barua's method to explore the field equations with an anisotropic fluid. We discuss models with positive matter density and pressure that satisfy all of the energy and stability conditions. It is found that charge does not vanish at the center of the cylinder. The equilibrium condition as well as the physical conditions are discussed. Further, we highlight the connection between our solutions and charged strange quark stars and dark matter including charged massive particles. A graphical analysis of the matter variables versus charge is given, which indicates a physically reasonable matter distribution. [ABSTRACT FROM AUTHOR]

The trajectory of a test particle or a photon around a general spherical black hole is studied, and bending of the light trajectory is investigated. A pseudo-Newtonian gravitational potential describing the gravitational field of the black hole is determined and is compared with the related effective potential for test particle motion. As an example, results are presented for a Reissner-Nordström black hole. [ABSTRACT FROM AUTHOR]

Polytropic gas spheres of index 1 and extremely high central densities are analysed with the help of general relativistic field equations. Parameters such as the radius and mass are calculated for different central densities. The limiting values of these quantities are obtained and the physical nature of sound waves in these bodies is verified. [ABSTRACT FROM AUTHOR]