Maximum bounds on the surface redshift of anisotropic stars

Иванов, Б. В.

doi:10.1103/physrevd.65.104011

Cited by 481 publications

(479 citation statements)

References 22 publications

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“…(vii) There are many other solutions of charged matter in various situations which have been discovered throughout the years. Many of them are interesting and would deserve a review, but there are too many to be quoted here, see [50] for a very partial list. (viii) Charged gravitating solutions have been also used to study Abraham type models for the electron, with and without Poincaré stresses see, e.g, [51,52,53], and also [3] and [17].…”

Section: Further Connectionsmentioning

confidence: 99%

Bonnor stars indspacetime dimensions

Lemos¹,

Zanchin

2008

Phys. Rev. D

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Bonnor stars are regular static compact configurations in equilibrium, composed of an extremal dust fluid, i.e., a charged dust fluid where the mass density is equal to the charge density in appropriate units and up to a sign, joined to a suitable exterior vacuum solution, both within Newtonian gravity and general relativity.In four dimensions, these configurations obey the Majumdar-Papapetrou system of equations, in one case, the system is a particular setup of Newtonian gravity coupled to Coulomb electricity and electrically charged matter or fluid, in the other case, the system is a particular setup of general relativity coupled to Maxwell electromagnetism and electrically charged matter or fluid, where the corresponding gravitational potential is a specially simple function of the electric potential field and the fluid, when there is one, is made of extremal dust. Since the Majumdar-Papapetrou system can be generalized to d spacetime dimensions, as has been previously done, and higher dimensional scenarios can be important in gravitational physics, it is natural to study this type of Bonnor solutions in higher dimensions, d ≥ 4. As a preparation, we analyze Newton-Coulomb theory with an electrically charged fluid in a Majumdar-Papapetrou context, in d = n + 1 spacetime dimensions, with n being the number of spatial dimensions. We show that within the Newtonian theory, in vacuum, the Majumdar-Papapetrou relation for the gravitational potential in terms of the electric potential, and its related Weyl relation, are equivalent, in contrast with general relativity where they are distinct. We study a class of spherically symmetric Bonnor stars within this theory. Under sufficient compactification they form point mass charged Newtonian singularities. We then study the analogue type systems in the Einstein-Maxwell theory with an electrically charged fluid. Drawing on our previous work on the d-dimensional Majumdar-Papapetrou system, we restate some properties of this system. We obtain spherically symmetric Bonnor star solutions in d = n + 1 spacetime dimensions. We show that these stars, under sufficient compactification, form d-dimensional quasi-black holes. We also show that in the appropriate low gravity limit theses solutions turn into the solutions of Newtonian gravity, i.e., they are quasi-Newtonian Bonnor stars. In this connection, we note that the star solutions in Majumdar-Papapetrou Newtonian gravity, when contrasted to those solutions in Majumdar-Papapetrou general relativity, display clearly the branching off of the high density objects that may arise in the strong field regime of each theory, mild singularities in one theory, quasi-black holes in the other. Another important feature worth of mention is that, whereas there are no solutions for Newtonian or relativistic stars supported by degenerate pressure in higher dimensions, higher dimensional Bonnor stars, supported by electric repulsion, do indeed have solutions within Newtonian gravity and general relativity. So the existence of stars in h...

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Section: Further Connectionsmentioning

confidence: 99%

Bonnor stars indspacetime dimensions

Lemos¹,

Zanchin

2008

Phys. Rev. D

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“…It is for this reason that many investigators use a variety of techniques to attain exact solutions. A comprehensive list of Einstein-Maxwell solutions, satisfying a variety of criteria for physical admissability, is provided by Ivanov [1]. The exact solutions may be used to study the physical features of charged spheroidal stars as demonstrated by Komathiraj and Maharaj [2], Sharma et al [3], Patel and Koppar [4], Patel et al [5], Tikekar and Singh [6] and Gupta and Kumar [7].…”

Section: Introductionmentioning

confidence: 99%

Classes of exact Einstein–Maxwell solutions

Komathiraj

Maharaj

2007

Gen Relativ Gravit

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We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein-Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

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“…Recently, Bhar [12,13] studied a new model of an anisotropic superdense star which admits conformal motions in the presence of a quintessence field which is characterized by a parameter w q with −1 < w q < −1/3. Charged anisotropic matter with linear equation of state [14,15] and a self gravitating, charged and anisotropic fluid sphere [16,17] were also considered For simplicity, we consider the static, spherically symmetric configurations. The stress tensor for an anisotropic fluid compatible with the spherical symmetry is…”

Section: Introductionmentioning

confidence: 99%

Black hole in closed spacetime with an anisotropic fluid

Kim¹

2017

Phys. Rev. D

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We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static and closed space exists only when the radial pressure is negative but its size is smaller than the density. The Einstein equation is eventually casted into a first order autonomous equation on two-dimensional plane of scale-invariant variables, which are equivalent to the Tolman-Oppenheimer-Volkoff (TOV) equation in general relativity. Then, we display various solution curves numerically. An exact solution describing a black hole solution in a closed spacetime was known in Ref. [1], which solution bears a naked singularity and negative energy era. We find that the two deficits can be remedied when ρ + 3p1 > 0 and ρ + p1 + 2p2 < 0, where the second violates the strong energy condition.

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Maximum bounds on the surface redshift of anisotropic stars

Abstract: It is shown that for realistic anisotropic star models the surface redshift can not exceed the values 3.842 or 5.211 when the tangential pressure satisfies the strong or the dominant energy condition respectively. Both values are higher than 2, the bound in the perfect fluid case. 04.20.Cv

Cited by 481 publications

References 22 publications

Bonnor stars indspacetime dimensions

Bonnor stars indspacetime dimensions

Classes of exact Einstein–Maxwell solutions

Black hole in closed spacetime with an anisotropic fluid

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