Stellar modeling with the Einstein-Maxwell field equations via gravitational decoupling

The aim of the present paper is to find an exact anisotropic and charged version of the well-known Heintzmann interior solution [Z. Phys. 228 (1969) 489] in a space-time via the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling). Further, we discuss the physical cogency of the solution for the coupled system by performing several physical tests. The obtained model represents the neutron star 4U1608-52 and fulfills all the requirements in order to be a well behaved physical solution to Einstein-Maxwell’s field equations.     

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.     

Geometry of the thermodynamics of the black holes in Ho<Emphasis Type="Italic">ř</Emphasis>ava-Lifshitz gravity

Recently, a non-relativistic renormalizable theory of gravity has been proposed by Hořava. This theory is essentially a field theoretic model for a UV complete theory of gravity and it reduces to Einstein’s general relativity at large distances. Subsequently, Cai and his collaborators have obtained black hole solution in this gravity theory and studied the thermodynamic properties of the black hole solutions. In present work, we investigate the geometric thermodynamics of the above black hole solutions and examine the possibilities of any phase transition.     

Collapsing shear-free radiating fluid spheres

We present a new class of exact solutions of relativistic field equations for a collapsing spherically symmetric shear-free isotopic fluid undergoing radial heat flow. The interior solutions are matched with Vaidya exterior metric over the boundary. Initially the interior solutions represent a static configuration of perfect fluid which then gradually starts evolving into radiating collapse.     

Exterior and interior metrics with quadrupole moment

We present the Ernst potential and the line element of an exact solution of Einstein’s vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass distribution. We show that in the limiting case of slowly rotating and slightly deformed configuration, there exists a coordinate transformation that relates the exact solution with the approximate Hartle solution. It is shown that this approximate solution can be smoothly matched with an interior perfect fluid solution with physically reasonable properties. This opens the possibility of considering the quadrupole moment as an additional physical degree of freedom that could be used to search for a realistic exact solution, representing both the interior and exterior gravitational field generated by a self-gravitating axisymmetric distribution of mass of perfect fluid in stationary rotation.     

多头螺旋槽管壁面液膜掺混时的流动状态

本文通过建立小流量液体在水平螺旋槽管外壁面液膜强化传热的拟线性模型,得到了壁面液膜发生流体掺混时液膜的厚度分布,并分析了相邻槽道间发生流体掺混的条件,以及发生流体掺混时液膜的形成过程。结果表明:多头螺旋槽管能够提供一个合适的几何倾斜表面,使得液体不仅能够沿着螺旋槽道流动,而且可以越过槽道的前后缘边界汇入下一个槽道,各螺旋槽道之间发生流体的相互掺混,即实现了二次分布,液膜厚度较掺混前更薄且分布更均匀。     

Anisotropic compact stars in Karmarkar spacetime

We present a new class of solutions to the Einstein field equations for an anisotropic matter distribution in which the interior space-time obeys the Karmarkar condition. The necessary and sufficient condition required for a spherically symmetric space-time to be of Class One reduces the gravitational behavior of the model to a single metric function. By assuming a physically viable form for the grr metric potential we obtain an exact solution of the Einstein field equations which is free from any singularities and satisfies all the physical criteria. We use this solution to predict the masses and radii of well-known compact objects such as Cen X-3, PSR J0348+0432, PSR B0943+10and XTE J1739-285.     

A spherically symmetric gravitational collapse-field with radiation

An interior spherically symmetric solution of Einstein’s field equations corresponding to perfect fluid plus a flowing radiation-field is presented. The physical 3-spacet=constant of our solution is spheroidal. Vaidya’s pure radiation field is taken as the exterior solution. The inward motion of the collapsing boundary surface follows from the equations of fit. An approximation procedure is used to get a generalization of the standard Oppenheimer-Snyder model of collapse with outflow of radiation. One such explicit solution has been given correct to second power of eccentricity of the spheroidal 3-space.     

A family of charged compact objects with anisotropic pressure

Utilizing an ansatz developed by Maurya et al. we present a class of exact solutions of the Einstein–Maxwell field equations describing a spherically symmetric compact object. A detailed physical analysis of these solutions in terms of stability, compactness and regularity indicates that these solutions may be used to model strange star candidates. In particular, we model the strange star candidate Her X-1 and show that our solution conforms to observational data to an excellent degree of accuracy. An interesting and novel phenomenon which arises in this model is the fact that the relative difference between the electromagnetic force and the force due to the pressure anisotropy changing sign within the stellar interior. This may be an additional mechanism required for stability against cracking of the stellar object.     

Exact Interior Solutions for Charged Fluid Spheres

A new method is discussed to obtain the interior solution of Einstein-Maxwell equations for a charged static sphere from a known particular solutions of a similar kind. Beginning with a charged fluid interior solution reported by Patel and Pandya [11], a new interior Reissner-Nördstrom metric is obtained using this method and physical aspects of it are extensively discussed.     

A new model for strange stars

In the present work, we attempt to find a new class of solutions for the spherically symmetric perfect fluid sphere by employing the homotopy perturbation method (HPM), a new tool via which the mass polynomial function facilitates to tackle the Einstein field equations. A set of interior solutions found on the basis of the simplest MIT bag model equation of state in the form \(p=\frac{1}{3}(\rho -4B)\) where B is the bag constant. The proposed interior metric for the stellar system is consistent with the exterior Schwarzschild spacetime on the boundary. In addition, we also conduct a detailed study on different tests, viz. the energy conditions, TOV equation, adiabatic index, Buchdahl limit, etc., to verify the physical validity of the proposed model. The numerical value of the used parameters are predicted for different strange star candidates, for different chosen values of the bag constant. In a nutshell, by exploiting HPM technique first time ever in the field of relativistic astrophysics, we have predicted in the present literature a singularity-free and stable stellar model which is suitable to describe ultra-dense objects, like strange (quark) stars.     

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.     

Incompressible Einstein–Maxwell fluids with specified electric fields

The Einstein–Maxwell equations describing static charged spheres with uniform density and variable electric field intensity are studied. The special case of constant electric field is also studied. The evolution of the model is governed by a hypergeometric differential equation which has a general solution in terms of special functions. Several classes of exact solutions are identified which may be considered as charged generalizations of the incompressible Schwarzschild interior model. An analysis of the physical features is undertaken for the uniform case. It is demonstrated that uniform density spheres with constant electric field intensity are not realizable with isotropic pressures. This highlights the necessity of studying the criteria for physical admissability of gravitating spheres in general relativity which are solutions to the Einstein–Maxwell equations.     

Relativistic compact stars with charged anisotropic matter

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.     

A study of detonation propagation and diffraction with compliant confinement

Previous computational studies of diffracting detonations with the ignition-and-growth (IG) model demonstrated that, contrary to experimental observations, the computed solution did not exhibit dead zones. For a rigidly confined explosive it was found that while diffraction past a sharp corner did lead to a temporary separation of the lead shock from the reaction zone, the detonation re-established itself in due course and no pockets of unreacted material remained. The present investigation continues to focus on the potential for detonation failure within the IG model, but now for a compliant confinement of the explosive. The aim of the present paper is two-fold. First, in order to compute solutions of the governing equations for multi-material reactive flow, a numerical method is developed and discussed. The method is a Godunov-type, fractional-step scheme which incorporates an energy correction to suppress numerical oscillations that occur near material interfaces for standard conservative schemes. The accuracy of the solution method is then tested using a two-dimensional rate-stick problem for both strong and weak confinements. The second aim of the paper is to extend the previous computational study of the IG model by considering two related problems. In the first problem, the corner-turning configuration is re-examined, and it is shown that in the matter of detonation failure, the absence of rigid confinement does not affect the outcome in a material way; sustained dead zones continue to elude the model. In the second problem, detonations propagating down a compliantly confined pencil-shaped configuration are computed for a variety of cone angles of the tapered section. It is found, in accord with experimental observation, that if the cone angle is small enough, the detonation fails prior to reaching the cone tip. For both the corner-turning and the pencil-shaped configurations, mechanisms underlying the behaviour of the computed solutions are identified.     

A Plane-Symmetric Inhomogeneous Cosmological Model of Perfect Fluid Distribution with Electromagnetic Field I

A plane-symmetric inhomogeneous cosmological model of perfect fluiddistribution with electro-magnetic field is obtained. F₁₂ is the non-vanishing component of electromagnetic field tensor. To get a deterministic solution, we assume the free gravitational field is Petrov type-II non-degenerate. Some physical and geometric properties of the model are also discussed.     

Properties of near and far fields for the electric line source illumination of a lossless metamaterial covered conductor cylinder

This work concentrated on an ELS (electric line source) radiating parallel to a lossless metamaterial covered infinitely long conductor cylinder. First, the exact analytical solution of the electromagnetic model is derived. Second, the numerical results based on the solution are given. Under different geometric and electromagnetic parameters, the patterns of the near field are obtained; the directivity and normalized radiation resistance are presented to discuss the properties of the far field. Because of the negative refraction of the metamaterial, it can be seen that there is a distinct “focus” in the metamaterial layer from the near field pattern, which does not exist in conventional material layer. The presented electromagnetic model is compared with the former, simpler model through the directivity and its validity is proven. PACS 78.70.Gq; 81.05.Zx; 84.40.Ba     

Variations in defect substructure and fracture surface of commercially pure aluminum under creep in weak magnetic field

Commercially pure polycrystalline aluminum of grade A85, as a test material, is investigated. Using scanning and transmission electron microscopy the aluminum fine structure and fracture surface are analyzed. Fractures are studied in the regime of creep with and without a simultaneous effect of 0.3-T magnetic field. It is found that the application of a magnetic field in a linear stage of creep leads to substructure imperfection increasing. Furthermore, the magnetic field effect on aluminum in the process of creep causes the average scalar density of dislocations to increase and induces the process of dislocation loop formation to strengthen. Fractographic investigation of the fracture surface shows that in the fibrous fracture zone the average size of plastic fracture pits decreases more than twice under creep in the condition of external magnetic field compared with in the conventional experimental condition. In a shear zone, the magnetic field causes the average size of fracture pits to decrease. Experimental data obtained in the research allow us to conclude that the magnetic field effect on aluminum in the process of creep leads to the fracture toughness value of the material decreasing, which will affect the state of defect substructure of the volume and surface layer of the material. The influence of the magnetic field is analyzed on the basis of the magneto-plasticity effect.     

Vortex structures with complex points singularities in two-dimensional Euler equations. New exact solutions

In this work we present a new class of exact stationary solutions for two-dimensional (2D) Euler equations. Unlike already known solutions, the new ones contain complex singularities. We consider point singularities which have a vector field index greater than 1 as complex. For example, the dipole singularity is complex because its index is equal to 2. We present in explicit form a large class of exact localized stationary solutions for 2D Euler equations with a singularity whose index is equal to 3. The solutions obtained are expressed in terms of elementary functions. These solutions represent a complex singularity point surrounded by a vortex satellite structure. We also discuss the motion equation of singularities and conditions for singularity point stationarity which provide the stationarity of the complex vortex configuration.