Stellar models with generalized pressure anisotropy

Sunzu, Jefta M.; Mathias, Alberto K; Maharaj, S. D.

doi:10.1007/s12036-019-9575-4

Cited by 38 publications

(16 citation statements)

References 35 publications

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“…up to order 6 of Taylor Series for in terms of r . Similar polynomial form of anisotropy ( = i X i r i ) can be found to study charged anisotropic system in several literatures [68][69][70][71]. The isotropic condition can be regained by choosing arbitrary constants to zero in their work.…”

Section: Einstein Field Equationsmentioning

confidence: 81%

“…Anisotropy in the form = 3 i=1 X i r i can be found in the work of Sunzu et al [70] for describing charged anisotropic stars. Anisotropy, = 5 i=1 X i r i have been discussed by Sunzu et al [71] and anisotropy in the form of = X 3 r 3 + X 4 r 4 is also fashioned in the work of Sunzu and Mahali [72]. As a limitation of our model, we can not generate the isotropic pressure condition from the specified anisotropic form.…”

Section: Einstein Field Equationsmentioning

confidence: 97%

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A new class of compact stellar model compatible with observational data

Das¹,

Rahaman

Baskey³

2019

Eur. Phys. J. C

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In this work, a physically reasonable metric potential g rr and a specific choice of the anisotropy has been utilized to obtain closed-form solutions of the Einstein field equation for a spherically symmetric anisotropic matter distribution. This class of solution has been used to develop viable models for observed pulsars. Smooth matching of interior spacetime metric with the exterior Schwarzschild metric and utilizing the condition that radial pressure is zero across the boundary leads us to determine the model parameters. A particular pulsar 4U 1820 − 30 having current estimated mass and radius (mass = 1.58M and radius = 9.1 km) has been allowed for testing the physical acceptability of the developed model. The gross physical nature of the observed pulsar has been analyzed graphically. The stability of the model is also discussed given causality conditions, adiabatic index and generalized Tolman-Oppenheimer-Volkov (TOV) equation under the forces acting on the system. To show that this model is compatible with observational data, few more pulsars have been considered, and all the requirements of a realistic star are highlighted. Additionally, the mass-radius (M-R) relationship of compact stellar objects analyzed for this model. The maximum mass for the presented model is ≈ 4M which is compared with the realization of Rhoades and Ruffini (Phys Rev Lett 32:324, 1974).

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Section: Einstein Field Equationsmentioning

confidence: 81%

Section: Einstein Field Equationsmentioning

confidence: 97%

A new class of compact stellar model compatible with observational data

Das¹,

Rahaman

Baskey³

2019

Eur. Phys. J. C

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“…Furthermore, we show that the anisotropy has a positive value which can be interpreted as a repulsive force. This fact is because the tangential pressure is greater than the radial pressure, i.e., p t > p r [130]. The issue of stability is studied and we showed that the derived model is stable against the different forces (gravitational, hydrostatic, anisotropic and electromagnetic) acting on it.…”

Section: Discussionmentioning

confidence: 92%

Stable and self-consistent compact star models in teleparallel gravity

Nashed

Capozziello

2020

Eur. Phys. J. C

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In the framework of Teleparallel Gravity, we derive a charged non-vacuum solution for a physically symmetric tetrad field with two unknown functions of radial coordinate. The field equations result in a closed-form adopting particular metric potentials and a suitable anisotropy function combined with the charge. Under these circumstances, it is possible to obtain a set of configurations compatible with observed pulsars. Specifically, boundary conditions for the interior spacetime are applied to the exterior Reissner–Nordström metric to constrain the radial pressure that has to vanish through the boundary. Starting from these considerations, we are able to fix the model parameters. The pulsar $$\textit{PSR J 1614-2230}$$ PSR J 1614 - 2230 , with estimated mass $$M= 1.97 \pm 0.04\, M_{\circledcirc },$$ M = 1.97 ± 0.04 M ⊚ , and radius $$R= 9.69 \pm 0.2$$ R = 9.69 ± 0.2 km is used to test numerically the model. The stability is studied, through the causality conditions and adiabatic index, adopting the Tolman–Oppenheimer–Volkov equation. The mass–radius (M, R) relation is derived. Furthermore, the compatibility of the model with other observed pulsars is also studied. We reasonably conclude that the model can represent realistic compact objects.

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“…Also, we show that the tangential pressure is greater from the radial pressure, p t > p r as shown in Figs. 10a which means that we have a repulsive force [81]. Moreover, we study the issue of stability and show in detail that our model is stable against the gravitational, hydrostatic, and anisotropic forces as Fig.…”

Section: Discussionmentioning

confidence: 89%

Neutral physical compact spherically symmetric stars with non-exotic matters in Einstein’s cluster model using Weitzenböck geometry

2020

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We revisit the neutral (uncharged) solutions that describe Einstein’s clusters with matters in the frame of Weitzenböck geometry. To this end, we use a tetrad field with non-diagonal spherical symmetry which gives vanishing of the off-diagonal components of the gravitational field equations. The cluster solutions are calculated by using an anisotropic energy–momentum tensor. We solve the field equations using two novel assumptions. First, we use an equation of state that relates density with tangential pressure, and then we assume a specific form of one of the metric potentials in addition to the assumption of the vanishing of radial pressure to make the system of differential equations in a closed-form. The resulting solutions are coincide with the literature $$ however \, \,in\, \,this\, \,study\, \,we\, \,constrain\,\, the\,\, constants \, \,of\, \, integration\, \, from\, \, \,the\, \, matching\,\, of\, \,boundary $$ h o w e v e r i n t h i s s t u d y w e c o n s t r a i n t h e c o n s t a n t s o f i n t e g r a t i o n f r o m t h e m a t c h i n g o f b o u n d a r y $$ condition\, \, in a\,\, way \,\,different\,\, from\,\, that\,\, presented \,\,in \,\,the\,\, literature. $$ c o n d i t i o n i n a w a y d i f f e r e n t f r o m t h a t p r e s e n t e d i n t h e l i t e r a t u r e . Among many things presented in this study, we investigate the static stability specification and show that our model is consistent with a real compact start except that the tangential pressure has a vanishing value at the center of the star which is not accepted from the physical viewpoint of a real compact star. We conclude that the model that has vanishing radial pressure in the frame of Einstein’s theory is not a physical model. Therefore, we extend this study and derive a new compact star without assuming the vanishing of the redial pressure but instead we assume new form of the metric potentials. We repeat our procedure done in the case of vanishing radial pressure and show in details that the new compact star is more realistic from different physical viewpoints of real compact stellar.

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Stellar models with generalized pressure anisotropy

Cited by 38 publications

References 35 publications

A new class of compact stellar model compatible with observational data

A new class of compact stellar model compatible with observational data

Stable and self-consistent compact star models in teleparallel gravity

Neutral physical compact spherically symmetric stars with non-exotic matters in Einstein’s cluster model using Weitzenböck geometry

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