Internal solution for stationary axially symmetric gravitational fields

Sedrakyan, D. M.; Chubaryan, Eh. V.

doi:10.1007/bf01013134

Cited by 6 publications

(5 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the sake of clarity, it should be mentioned that the structure equations describing uniformly rotating configurations, as derived in general relativity by Hartle in [12], reduce identically to the equations shown in this work for  ¥ c . Correspondingly, the structure equations formulated by Sedrakyan and Chubaryan [45] in general relativity also reduce to their Newtonian counterparts in the corresponding limiting case [22]. The mathematical and physical equivalence of these two formalisms has been recently shown in [46] by comparing the exterior Hartle-Thorne [47] and the Sedrakyan Chubaryan [45] solutions.…”

Section: Comparison With Other Results In the Literaturementioning

confidence: 92%

“…Correspondingly, the structure equations formulated by Sedrakyan and Chubaryan [45] in general relativity also reduce to their Newtonian counterparts in the corresponding limiting case [22]. The mathematical and physical equivalence of these two formalisms has been recently shown in [46] by comparing the exterior Hartle-Thorne [47] and the Sedrakyan Chubaryan [45] solutions. Thus, the difference in numbers of these two approaches in table 2 can be due to the numerical integrations, only.…”

Section: Comparison With Other Results In the Literaturementioning

confidence: 92%

See 1 more Smart Citation

Hartle formalism for rotating Newtonian configurations

et al. 2016

View full text Add to dashboard Cite

We apply the Hartle formalism to study equilibrium configurations in the framework of Newtonian gravity. This approach allows one to study in a simple manner the properties of the interior gravitational field in the case of static as well as stationary rotating stars in hydrostatic equilibrium. It is shown that the gravitational equilibrium conditions reduce to a system of ordinary differential equations which can be integrated numerically. We derive all the relevant equations up to the second order in the angular velocity. Moreover, we find explicitly the total mass, the moment of inertia, the quadrupole moment, the polar and equatorial radii, and the eccentricity of the rotating body. We also present the procedure to calculate the gravitational Love number. We test the formalism in the case of white dwarfs and show its compatibility with the known results in the literature.

show abstract

Section: Comparison With Other Results In the Literaturementioning

confidence: 92%

Section: Comparison With Other Results In the Literaturementioning

confidence: 92%

Hartle formalism for rotating Newtonian configurations

et al. 2016

View full text Add to dashboard Cite

show abstract

“…21 A method to compute RWDs configurations accurate up to second order in the angular velocity of a star Ω was developed by two of the authors (see Ref. 22 for details), independently of the work of Hartle(1967. ) 12 In Arutyunyan et.…”

Section: Resultsmentioning

confidence: 99%

General Relativistic and Newtonian White Dwarfs

Boshkayev

Rueda

Ruffini

et al. 2015

The Thirteenth Marcel Grossmann Meeting

View full text Add to dashboard Cite

The properties of uniformly rotating white dwarfs (RWDs) are analyzed within the framework of Newton's gravity and general relativity. In both cases Hartle's formalism is applied to construct the internal and external solutions to the field equations. The white dwarf (WD) matter is described by the Chandrasekhar equation of state. The region of stability of RWDs is constructed taking into account the mass-shedding limit, inverse β-decay instability, and the boundary established by the turning points of constant angular momentum J sequences which separates stable from secularly unstable configurations. We found the minimum rotation period ∼ 0.28 s in both cases and maximum rotating masses ∼ 1.534M ⊙ and ∼ 1.516M ⊙ for the Newtonian and general relativistic WDs, respectively. By using the turning point method we show that general relativistic WDs can indeed be axisymmetrically unstable whereas the Newtonian WDs are stable.

show abstract

“…It was shown that the discrepancies between the Hartle formalism and exact numerical computations appear close to the mass shedding limit. In addition, it has been demonstrated that the so-called Sedrakyan and Chubaryan formalism [9,10], usually applied to the study of rigidly rotating WDs and NSs, is identical with the Hartle formalism [35]. Therefore, one can safely employ the Hartle formalism at the mass shedding limit for rough estimates and qualitative analyses [36,37].…”

Section: Problem Setup and Methodologymentioning

confidence: 99%

“…The physical properties of WDs have been intensively studied both in Newtonian gravity (NG) and general relativity (GR) [2, 3,[9][10][11][12][13][14]. It has been shown that the effects of GR are crucial to analyze the stability of WDs close to the Chandrasekhar mass limit 1.44M  and can be neglected for low mass WDs [6].…”

Section: Introductionmentioning

confidence: 99%

Static and rotating white dwarf stars at finite temperatures

Boshkayev¹,

Luongo²,

Muccino³

et al. 2021

ijmph

View full text Add to dashboard Cite

Static and rotating, cold and hot white dwarf stars are investigated both in Newtonian gravity and general theory of relativity, employing the well-established Chandrasekhar equation of state. The Hartle formalism is involved to construct and study uniformly rotating configurations of white dwarfs. The mass-radius, mass-central density, radius-central density and other basic relations of stable white dwarfs, consisting of pure helium and iron, are constructed for different temperatures at mass shedding limit. Stability of white dwarfs is analyzed with respect to the inverse beta decay process, pycnonuclear reactions and instabilities of general relativity. It is found that for a fixed mass hot white dwarfs consisting of pure iron are smaller in size, correspondingly denser with respect to the ones composed of light elements. In addition, it is shown that near the Chandrasekhar mass limit the mass of hot rotating white dwarfs is slightly less than for cold ones, though for low mass rotating white dwarfs and static ones in all mass range the situation is opposite.

show abstract

Internal solution for stationary axially symmetric gravitational fields

Cited by 6 publications

References 2 publications

Hartle formalism for rotating Newtonian configurations

Hartle formalism for rotating Newtonian configurations

General Relativistic and Newtonian White Dwarfs

Static and rotating white dwarf stars at finite temperatures

Contact Info

Product

Resources

About