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Negi, P. S.; Durgapal, M. C.

doi:10.1023/a:1002707730439

Cited by 22 publications

(42 citation statements)

References 24 publications

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“…It has been extensively employed to neutron star studies while its physical realization has been examined in detail very recently [24]. Actually, the stability of this solution has been examined by Negi et al [26,27]. In the present work the stability is reexamined and in addition the results are compared with the other similar solutions.…”

Section: Tolman VII Solutionmentioning

confidence: 88%

“…In particular, the Tolman VII solution is the most popular one, with applications in various problems related to very compact object (in contradiction with the Tolman's statement [15] that this solution, due to the complicate dependence of the pressure on the distance r, is not a convenient one for physical consideration). The stability of the Tolman VII solution has been examined by Negi [26,27]. It was found that the solution is stable for a large range of the compactness parameter β = GM/Rc 2 .…”

Section: Introductionmentioning

confidence: 99%

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The stability of relativistic stars and the role of the adiabatic index

Moustakidis

2017

Gen Relativ Gravit

183

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We study the stability of three analytical solutions of the Einstein's field equations for spheres of fluid. These solutions are suitable to describe compact objects including white dwarfs, neutron stars and supermassive stars and they have been extensively employed in the literature. We re-examine the range of stability of the Tolman VII solution, we focus on the stability of the Buchdahl solution which is under contradiction in the literature and we examine the stability of the Nariai IV solution. We found that all the mentioned solutions are stable in an extensive range of the compactness parameter. We also concentrate on the effect of the adiabatic index on the instability condition. We found that the critical adiabatic index, depends linearly on the ratio of central pressure over central energy density Pc/Ec, up to high values of the compactness. Finally, we examine the possibility to impose constraints, via the adiabatic index, on realistic equations of state in order to ensure stable configurations of compact objects.

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Section: Tolman VII Solutionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

The stability of relativistic stars and the role of the adiabatic index

Moustakidis

2017

Gen Relativ Gravit

183

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“…Analytic solutions for modeling more realistic stars include Buchdahl [1,19,20] and Tolman VII [1,21,22] solutions. The latter is stable for a large range of compactness [23] and its geometric structures were studied in [24,25].…”

Section: Introductionmentioning

confidence: 99%

Improved analytic modeling of neutron star interiors

Jiang

Yagi

2019

Phys. Rev. D

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Studies of neutron stars are extremely timely given the recent detection of gravitational waves from a binary neutron star merger GW170817, and an International Space Station payload NICER currently in operation that aims to determine radii of neutron stars to a precision better than 5%. In many cases, neutron star solutions are constructed numerically due to the complexity of the field equations with realistic equations of state. However, in order to relate observables like the neutron star mass and radius to interior quantities like central density and pressure, it would be useful to provide an accurate, analytic modeling of a neutron star interior. One such solution for static and isolated neutron stars is the Tolman VII solution characterized only by two parameters (e.g. mass and radius), though its agreement with numerical solutions is not perfect. We here introduce an improved analytic model based on the Tolman VII solution by introducing an additional parameter to make the analytic density profile agree better with the numerically obtained one. This additional parameter can be fitted in terms of the stellar mass, radius and central density in an equationof-state-insensitive way. In most cases, we find that the new model more accurately describes realistic profiles than the original Tolman VII solution by a factor of 2-5. Our results are first-step calculations towards constructing analytic interior solutions for more realistic neutron stars under rotation or tidal deformation. arXiv:1904.05954v3 [gr-qc]

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“…This ‘abnormality’ can be specified as (i) the pressure vanishes at average nuclear densities, and (ii) the speed of sound is equal to that of light even when the pressure is vanishingly small. This ‘abnormality’ can be removed if we ensure continuity of pressure, density and both of the metric parameters at the boundary of the structure (Negi & Durgapal 2000).…”

Section: Introductionmentioning

confidence: 99%

Hydrostatic equilibrium of causally consistent and dynamically stable neutron star models

Negi

2008

Monthly Notices of the Royal Astronomical Society

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We show that the mass–radius (M–R) relation corresponding to the stiffest equation of state (EOS) does not provide the necessary and sufficient condition of dynamical stability for equilibrium configurations, because such configurations cannot satisfy the ‘compatibility criterion’. In this regard, we construct sequences composed of core–envelope models such that, like the central condition belonging to the stiffest EOS, each member of these sequences satisfies the extreme case of the causality condition, v=c= 1, at the centre. We thereafter show that the M–R relation corresponding to the said core–envelope model sequences can provide the necessary and sufficient condition of dynamical stability only when the ‘compatibility criterion’ for these sequences is ‘appropriately’ satisfied. However, the ‘compatibility criterion’ can remain satisfied even when the M–R relation does not provide the necessary and sufficient condition of dynamical stability for the equilibrium configurations. In continuation of the results of a previous study, these results explicitly show that the ‘compatibility criterion’independently provides, in general, the necessary and sufficient condition of hydrostatic equilibrium for any regular sequence. In addition to its fundamental result, this study can explain simultaneously the higher and the lower values of the glitch healing parameter observed for the Crab‐like and Vela‐like pulsars respectively, on the basis of the starquake model of glitch generation.

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Untitled

Cited by 22 publications

References 24 publications

The stability of relativistic stars and the role of the adiabatic index

The stability of relativistic stars and the role of the adiabatic index

Improved analytic modeling of neutron star interiors

Hydrostatic equilibrium of causally consistent and dynamically stable neutron star models

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