A family of static solutions of the Einstein field equations with spherical symmetry for a locally anisotropic fluid with homogeneous energy density is obtained. These solutions depend on two adjustable parameters related to degree of anisotropy of the fluid. Some known solutions may be recovered for specific values of these parameters. As a difference to other known solutions it is possible to change the grade of anisotropy of the model, keeping the same functional dependence on the coordinates. By means of a slow adiabatic contraction, the stability of the obtained solutions is studied. Also, it is shown, how it is possible to enhance the stability of the models by adjusting the parameters, and to obtain more compact configurations than those obtained with other similar anisotropic solutions, while the dominant or strong energy condition holds within the sphere.

In this work, a spherically symmetric and static relativistic anisotropic fluid sphere solution of the Einstein field equations is provided. To build this particular model, we have imposed metric potential $$e^{2\lambda (r)}$$e2λ(r) and an equation of state. Specifically, the so-called modified generalized Chaplygin equation of state with $$\omega =1$$ω=1 and depending on two parameters, namely, A and B. These ingredients close the problem, at least mathematically. However, to check the feasibility of the model, a complete physical analysis has been performed. Thus, we analyze the obtained geometry and the main physical observables, such as the density $$\rho $$ρ, the radial $$p_{r}$$pr, and tangential $$p_{t}$$pt pressures as well as the anisotropy factor $$\Delta $$Δ. Besides, the stability of the system has been checked by means of the velocities of the pressure waves and the relativistic adiabatic index. It is found that the configuration is stable in considering the adiabatic index criteria and is under hydrostatic balance. Finally, to mimic a realistic compact object, we have imposed the radius to be $$R=9.5\ [km]$$R=9.5[km]. With this information and taking different values of the parameter A the total mass of the object has been determined. The resulting numerical values for the principal variables of the model established that the structure could represent a quark (strange) star mixed with dark energy.

We extend the work of Mafa Takisa and Maharaj (2013) by considering Van der Waals modified equation of state with polytropic exponent for anisotropic matter distribution in the study of a compact relativistic objects. New exact solutions for Einstein-Maxwell equations are generated in terms of elementary functions. The behaviour of physical variables as energy density, charge density and radial pressure is consistent with seminal treatments which suggest relevance in the description of relativistic compact stars.

In this paper, we studied the behaviour of compact relativistic objects with anisotropic matter distribution considering quadratic equation of state of Feroze and Siddiqui (2011). We specify the gravitational potential Z(x) in order to integrate the fields equations and there has been calculated the energy density, the radial pressure, the anisotropy and the mass function. The new solutions to the Einstein-Maxwell system of equations are found in term of elementary functions. For n=2, we have obtained the expressions for mass function, energy density, radius and metric functions of the model of Thirukkanesh and Ragel (2012) with polytropic equation of state.

This article shows novel model Pauli-Dirac-Planck-quantum-circuit-assembly-gage, consisting of the monopole quasiparticles and electron-positron particle fields, demonstrating power of Iyer Markoulakis Helmholtz Hamiltonian mechanics of point vortex and gradient fields general formalism. Transforming this general metrics to Coulombic gaging metrics and performing gage charge fields calculations, derivation of assembly eigenvector matrix bundle constructs of magnetic monopoles, and electron positron particle gage metrics were successfully compiled, like SUSY (?( 1 &?@?*&1 )) Hermitian quantum matrix., modified to asymmetric strings gage metrics to account for asymmetrical magnetic pole forces measurements recently in physics. Physical analysis with graphics discussing scenarios of electric tensor particles and magnetic tensor monopoles permutationally interacting, figures showing simulations of fermions’ spins with Clifford algebraic geometry, and the graphs explaining vortex sinusoidal pulsed signal output distribution profile of typical equivalent wave velocity of the related point fields partially verify this quantum circuity assembly model. Table shows estimated size of this assembly greater than 10-34 Planck unit and less than quasi-particle size of 10-26 metrics unit. Wide-ranging applications of this quantum circuitry assembly model exist for quantum supercomputing expertise antenna networks, alongside quantum astrophysical grand unifying genesis of electromagnetic gravitational matter antimatter systems. This quantum model can be verified by experimental techniques, such as spin-ice and Bose-Einstein condensate spinors.

Abstract:In this paper, have been found new class of solutions to the Einstein-Maxwell system for charged anisotropic matter which are relevant in the description of highly compact stellar objects. The equation of state is barotropic with a linear relation between the radial pressure and the energy density and we have considered a prescribed form for the gravitational potential Z. Variables as the energy density, radial pressure and the metric coefficients are written in terms of elementary and polynomial functions. The obtained models not admit singularities in the matter and the charge density.

In this work, water is captured as regular fluid with suspension of two types of hybrid nanoparticles, namely molybdenumdisulfide (MoS2) and graphene oxide (GO). The impact of Lorentz’s forces on mixed convective boundary-layer flow (BLF) is studied through an upright cylinder under the influences of thermal radiation. The shape factor is also assessed. The mathematical model for hybrid nanofluidis developed and, by implementing suitable similarity variables, the leading partial differential equations (PDEs) are altered into a non-linear ordinary differential equations (ODEs) system and then resolved through a bvp4c solver. The penetrations of varied parameters, such as thermal radiation, nanomaterials shapes (bricks, platelets, bricks and cylinders), magneto-hydrodynamics (MHD), and ratio parameters on the temperature and fluid velocity, along with the skin friction and the Nusselt number, are typified qualitatively via sketches. The opposing flow, as well as the assisting flow, is considered. The results indicate that the impact of hybrid nanofluid (HBNF) on the velocity and the temperature is more than nanofluid (NF). It is also scrutinized that the blade-shaped nanomaterials of hybrid nanofluid have a maximum temperature and brick-shaped nanomaterials have a low temperature. In addition, the friction factor and the heat transport rate decline due to the magnetic parameter and increase due to the shape factor. Moreover, the radiation uplifts the velocity and temperature, while the free stream Reynolds number declines the velocity and temperature. Finally, a comparison with available results in the literature are made and found in an excellent way. The ranges of constraints in this research are considered as: 0.01 ≤ λ ≤ 0.2 , 0 ≤ M ≤ 4 , 0 ≤ α ≤ 1.5 , 0 ≤ R d ≤ 1 , 1 ≤ Re a ≤ 3 , 0 ≤ ϕ 1 ≤ 0.1 and 0 ≤ ϕ 2 ≤ 0.003 .

Abstract:We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for anisotropic neutral fluid, compatible with a super dense star modeling by considering a specific choice of anisotropy factor  that includes a positive constant "" defined as anisotropy parameter, which varies the relation between the radial and tangential pressure. Further, we have constructed a super-dense star model with all degree of suitability. We have found that the maximum mass decreases with the increase of anisotropy parameter (α). The robustness of our result is that it matches with the recent discoveries.