On the Newtonian anisotropic configurations

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

doi:10.1140/epjc/s10052-015-3478-6

Cited by 18 publications

(20 citation statements)

References 11 publications

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“…A Newtonian approach is sufficient to study stellar structures in a comparatively low-density regime. However, in the case of compact stellar structures in the high-density regime, a general relativistic treatment is necessary, and the impact of anisotropy cannot be neglected while modelling such systems, see for example [1][2][3][4] and references therein. Ruderman [5] and Canuto [6] observed that material distribution in the highly dense core of a compact star might exhibit unequal stresses.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: an algorithm

Thirukkanesh¹,

Ragel

Sharma³

et al. 2018

Eur. Phys. J. C

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We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as an anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted.

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Section: Introductionmentioning

confidence: 99%

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: an algorithm

Thirukkanesh¹,

Ragel

Sharma³

et al. 2018

Eur. Phys. J. C

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“…Following [3], we assume that the presence of ∆ does not change the forms of isotropic Lane-Emden equations and it only modifies the coefficients of these equations. To do this, noting equation (18), we introduce a constant m such that (hereafter we set c = 1): 2q 0 (n + 1)dθ − 4∆ rρ 0 θ n dr = 2q 0 (m + 1)dθ (39)…”

Section: An Exact Solutionmentioning

confidence: 99%

“…The effect of anisotropy can be studied both in Newtonian gravity and General Relativity. For the configurations with not extremely high densities, the presence of anisotropy factor has been discussed in Newtonian regime [1,2,3] and otherwise general relativity must be used.…”

Section: Introductionmentioning

confidence: 99%

“…In 1972 Ruderman [4] for the first time argued that the nuclear matter may have anisotropic features in very high density regime (> 10 15 gr cm 3 ) and thus the nuclear interaction needs to be treated under relativistic point of view. After the pioneering work of Bowers and Liang [5] in 1974, the study of anisotropic distribution of matter got wide attention.…”

Section: Introductionmentioning

confidence: 99%

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On the relativistic anisotropic configurations

2016

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In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behavior of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed.

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“…A study of the more general hydrostatic equilibrium equations, considering pressure anisotropy, demonstrates that anisotropy can have a fundamental effect on the maximum equilibrium mass and gravitational surface red-shift [8][9][10]. At not very high densities, the effect of anisotropy can be analyzed in the context of Newtonian gravity [11,12]. At higher densities i.e., when ρ ≥ 10 15 g/cm 3 , both the GR effects and the relativistic effects become more important [7,[13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic compact stars via embedding approach in general relativity: new physical insights of stellar configurations

2021

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The main focus of this paper is to explore the possibility of providing a new family of exact solutions for suitable anisotropic spherically symmetric systems in the realm of general relativity involving the embedding spherically symmetric static metric into the five-dimensional pseudo-Euclidean space. In this regard, we ansatz a new metric potential $$\lambda (r)$$ λ ( r ) , and we obtained the other metric potential $$\nu (r)$$ ν ( r ) by mains of embedding class one approach. The unknown constants are determined by the matching of interior space-time with the Schwarzschild exterior space-time. The physical acceptability of the generating celestial model for anisotropic compact stars is approved via acting several physical tests of the main salient features viz., energy density, radial and tangential pressures, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability, which are well-compared with experimental statistics of four different compact stars: PSR J1416-2230, PSR J1903+327, 4U 1820-30 and Cen X-3. Conclusively, all the compact stars under observations are realistic, stable, and are free from any physical or geometrical singularities. We find that the embedding class one solution for anisotropic compact stars is viable and stable, plus, it provides circumstantial evidence in favor of super-massive pulsars.

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On the Newtonian anisotropic configurations

Cited by 18 publications

References 11 publications

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: an algorithm

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: an algorithm

On the relativistic anisotropic configurations

Anisotropic compact stars via embedding approach in general relativity: new physical insights of stellar configurations

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