An electromagnetic extension of the Schwarzschild interior solution and the corresponding Buchdahl limit

In this work we study the properties of compact spheres made of a charged perfect fluid with a MIT bag model EoS for quark matter. Considering static spherically symmetric spacetime we derive the hydrostatic equilibrium equations in the recently formulated four dimensional Einstein–Gauss–Bonnet (4D EGB) gravity theory. In this setting, the modified TOV equations are solved numerically with the aim to investigate the impact of electric charge on the stellar structure. A nice feature of 4D EGB theory is that the Gauss–Bonnet term has a non-vanishing contribution to the gravitational dynamics in 4D spacetime. We therefore analyse the effects of Gauss–Bonnet coupling constant $$\alpha $$ α and the charge fraction $$\beta $$ β on the mass–radius ($$M{-}R$$ M - R ) diagram and also the mass–central density $$(M{-}\rho _c)$$ ( M - ρ c ) relation of quark stars. Finally, we conclude that depending on the choice of coupling constant one could have larger mass and radius compared with GR and can also be relevant for more massive compact objects due to the effect of the repulsive Coulomb force.

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“…[77]. For in depth discussions about the stability of charged spheres have been found in [79][80][81][82]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Electrically charged quark stars in 4D Einstein–Gauss–Bonnet gravity

Pretel

Pradhan²,

Banerjee³

2022

Eur. Phys. J. C

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“…The first interior solution of the Einstein gravitational field equations was obtained by Schwarzschild in 1916 [61] under the assumption of the constant density of the star. It has a remarkable mathematical simplicity, and despite the fact that it is generally considered as not providing a realistic description of neutron stars, its properties have been intensively investigated [62]. In particular, for constant density stars the Buchdahl bound becomes exact, so that 2M/R = 8/9.…”

Section: A Constant Density Starsmentioning

confidence: 99%

Compact stars in the Einstein dark energy model

Haghani,

Harko

2022

Preprint

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We investigate the properties of high density compact objects in a vector type theory, inspired by Einstein's 1919 theory of elementary particles, in which Einstein assumed that elementary particles are held together by gravitational as well as electromagnetic type forces. From a modern perspective, Einstein's theory can be interpreted as a vector type model, with the gravitational action constructed as a linear combination of the Ricci scalar, of the trace of the matter energy-momentum tensor, and of a massive self-interacting vector type field. To obtain the properties of stellar models we consider the field equations for a static, spherically symmetric system, and we investigate numerically their solutions for different equations of state of quark and neutron matter, by assuming that the selfinteraction potential of the vector field either vanishes, or is quadratic in the vector field potential. We consider quark stars described by the MIT bag model equation of state, and in the Color Flavor Locked (CFL) phase, as well as compact stars consisting of a Bose-Einstein Condensate of neutron matter, with neutrons forming Cooper pairs. Constant density stars, representing a generalization of the Interior Schwarzschild solution of general relativity, are also analyzed. As an example of stars described by equations of state obtained by using effective nuclear interactions of the Skyrme type we consider the Douchin-Haensel (SLy) equation of state. The numerical solutions are explicitly obtained in both standard general relativity, and the Einstein dark energy model, and an in depth comparison between the astrophysical predictions of these two theories are performed. As a general conclusion of our study we find that for all the considered equations of state a much larger variety of stellar structures can be obtained in the Einstein dark energy model, including classes of stars that are more massive than their general relativistic counterparts. As a concrete applications of our results we suggest that compact objects with masses of the order of 2.5M⊙, associated, for example, with the GW 190814 gravitational wave event, could be in fact quark or neutron stars, described by the Einstein dark energy model.

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“…The probe also prescribes an upper bound on the charge to mass ratio Q 2 /M 2 ≤ 9/8. In a recent article, by developing a model for charged star which was shown to be a generalization of the uniform density Schwarzschild interior solution, Sharma et al [3] regained the charged analogue of the Buchdahl compactness bound…”

Section: Introductionmentioning

confidence: 99%

Anisotropic generalization of Buchdahl bound for specific stellar models

et al. 2021

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Anisotropy is one factor that appears to be significantly important in the studies of relativistic compact stars. In this paper, we make a generalization of the Buchdahl limit by incorporating an anisotropic effect for a selected class of exact solutions describing anisotropic stellar objects. In the isotropic case of a homogeneous distribution, we regain the Buchdahl limit $$2M/R \le 8/9$$ 2 M / R ≤ 8 / 9 . Our investigation shows a direct link between the maximum allowed compactness and pressure anisotropy vi-a-vis geometry of the associated 3-space.

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An electromagnetic extension of the Schwarzschild interior solution and the corresponding Buchdahl limit

Cited by 22 publications

References 39 publications

Electrically charged quark stars in 4D Einstein–Gauss–Bonnet gravity

Electrically charged quark stars in 4D Einstein–Gauss–Bonnet gravity

Compact stars in the Einstein dark energy model

Anisotropic generalization of Buchdahl bound for specific stellar models

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