On the relativistic anisotropic configurations

Shojai, Fatimah; Kohandel, M.; Степанян, А. А.

doi:10.1140/epjc/s10052-016-4204-8

Cited by 10 publications

(13 citation statements)

References 46 publications

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“…It can replace one of them. It is also equivalent to the Bianchi identities T µ ν;µ = 0, which in the static spherically symmetric case have only one non-trivial component [2], [58], [59], [60]. In CGS units G = 6.674 × 10 −8 cm 3 /g.s 2 , c = 3 × 10 10 cm/s, k = 2.071 × 10 −48 s 2 /g.cm, kc 2 = 1.864 × 10 −27 cm/g.…”

Section: Field Equations and Definitionsmentioning

confidence: 99%

A conformally flat realistic anisotropic model for a compact star

Иванов

2018

Eur. Phys. J. C

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Section: Field Equations and Definitionsmentioning

confidence: 99%

A conformally flat realistic anisotropic model for a compact star

Иванов

2018

Eur. Phys. J. C

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“…This is because the isotropic pressure, determined according to Eq. (10), decreases considerably slower with the radial coordinate r compared to that determined from the common TOV equation (3). Another peculiarity is that the total mass M decreases with the central pressure p 0 for the whole range of the central pressures under consideration, contrary to the stability constraint dM dp 0 > 0.…”

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confidence: 86%

“…Such an approach was followed recently, e.g., in Refs. [3,4]. Yet another strategy was suggested in Ref.…”

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confidence: 99%

Comment on “Covariant Tolman-Oppenheimer-Volkoff equations. II. The anisotropic case”

Isayev

2018

Phys. Rev. D

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Recently, the covariant formulation of the Tolman-Oppenheimer-Volkoff (TOV) equations for studying the equilibrium structure of a spherically symmetric compact star in the presence of the pressure anisotropy in the interior of a star was presented in Ref.[1] [Phys. Rev. D 97 (2018) 124057]. It was suggested there that the anisotropic solution of these equations can be obtained by finding, first, the solution of the common TOV equations for the isotropic pressure, and then by solving the differential equation for the anisotropic pressure whose particular form was established on the basis of the covariant TOV equations. It turns out that the anisotropic pressure determined according to this scheme has a nonremovable singularity Π ∼ 1 r 2 in the center of a star, and, hence, the corresponding anisotropic solution cannot represent a physically relevant model of an anisotropic compact star. A new scheme for constructing the anisotropic solution, based on the covariant TOV equations, is suggested, which leads to the regularly behaved physical quantities in the interior of a star. A new algorithm is applied to build model anisotropic strange quark stars with the MIT bag model equation of state. * isayev@kipt.kharkov.ua

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“…where ̺ is the mass (baryon) density, K is some constant, which can be, in principle, temperature dependent, γ is the polytropic exponent, n is the polytropic index. Note that in some works [12,36,38,41] the polytropic EoS is set in the form p r = Kε γ , which will not be considered here. It is possible to show (see, e.g., Ref.…”

Section: Generalized Lane-emden Equationsmentioning

confidence: 99%

“…Anisotropic spheres with the uniform energy density in general relativity were studied in Refs. [12,44], and with the variable energy density in Ref. [45].…”

Section: Introductionmentioning

confidence: 99%

General relativistic polytropes in anisotropic stars

Isayev

2017

Phys. Rev. D

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Spherically symmetric relativistic stars with the polytropic equation of state (EoS), which possess the local pressure anisotropy, are considered within the framework of general relativity. The generalized Lane-Emden equations are derived for the arbitrary anisotropy parameter $\Delta=p_t-p_r$ ($p_t$ and $p_r$ being the transverse and radial pressure, respectively). They are then applied to some special ansatz for the anisotropy parameter in the form of the differential relation between the anisotropy parameter $\Delta$ and the metric function $\nu$. The analytical solutions of the obtained equations are found for incompressible fluid stars and then used for getting their mass-radius relation, gravitational and binding energy. Also, following the Chandrasekhar variational approach, the dynamical stability of incompressible anisotropic fluid stars with the polytropic EoS against radial oscillations is studied. It is shown that the local pressure anisotropy with $p_t>p_r$ can make the incompressible fluid stars unstable with respect to radial oscillations, in contrast to incompressible isotropic fluid stars with the polytropic EoS which are dynamically stable.Comment: 27 pages, including 4 figures and 2 table

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On the relativistic anisotropic configurations

Cited by 10 publications

References 46 publications

A conformally flat realistic anisotropic model for a compact star

A conformally flat realistic anisotropic model for a compact star

Comment on “Covariant Tolman-Oppenheimer-Volkoff equations. II. The anisotropic case”

General relativistic polytropes in anisotropic stars

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