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.
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