Static spherically symmetric stiff matter in general relativity

Haggag, Salah; Hajj-Boutros, Joseph

doi:10.1088/0264-9381/11/4/003

Cited by 9 publications

(12 citation statements)

References 8 publications

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“…Therefore by using the matrix method we have rediscovered this exact solution for the stiff fluid matter that was obtained by Haggag and Hajj-Boutros [18].…”

Section: Three Classes Of Solutions Of the Static Field Equationsmentioning

confidence: 99%

Relativistic compact objects in isotropic coordinates

Mak

Harkó

2005

Pramana - J Phys

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We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type fluid with an equation of state p = γρ is discussed in detail.

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“…Therefore by using the matrix method we have rediscovered this exact solution for the stiff fluid matter that was obtained by Haggag and Hajj-Boutros [18].…”

Section: Three Classes Of Solutions Of the Static Field Equationsmentioning

confidence: 99%

Relativistic compact objects in isotropic coordinates

Mak

Harkó

2005

Pramana - J Phys

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“…The particular case, γ = 2, is the HHG solution [1] and in this case the HVF X becomes orthogonal to the fluid four-velocity, and for γ = 1 the space-time is obviously flat.…”

Section: Case (Ii)mentioning

confidence: 99%

“…In a recent paper, Haggag and Hajj-Boutros [1] presented a static, spherically symmetric perfect fluid solution with a stiff-matter type equation of state (i.e. : p = µ).…”

mentioning

confidence: 99%

“…The purpose of this letter is to give all the static, spherically symmetric perfect fluid solutions admitting a homothety. This family can be completely characterized by means of a real parameter γ (arising quite naturally from the equation of state for these fluids, see below), which must be in the interval [1,2] in order to satisfy energy conditions. The two limiting values of γ, namely γ = 1 and γ = 2 correspond to Minkowski flat space-time and to the HHB solution respectively.…”

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confidence: 99%

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Self-similar static solutions admitting a 2-space of constant curvature

Carot¹,

Sintes²

1994

Class. Quantum Grav.

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The plupose of thii letter is to give all the static, splierically symmehic perfect fluid solutions admitting a homothety. This family can be completely characterized by means of a real parameter y (arising quite naturally from the equation of state for these fluids, see below), which must be in the interval [ I , 21 in order to satisfy energy conditions. The two limiting values of y. namely y = 1 and y = 2 correspond to Minkowski flat spacetime and to the HHB solution, respectively.A few remarks concerning the similarity group and its action are in order here. It is a well known fact that an r-parameter group of homotheties H, (in which at least one proper homothety exists) always admits an (r -l)-parameter subgroup of isomehies G,-I. Now, the maximal dimension of the group of homotheties that a perfect fluid spacetime may admit is r = 7, in which case it is one of the special Robertson-Walker spacetimes [2], and therefore they are all known. The case r = 6 is not compatible with an energy-momentum tensor of the perfect-fluid type; thus, apart from the special Robertson-Waker solutions mentioned above, the highest dimension of the group of homotheties that a perfect fluid spacetime may admit is r = 5. In such case, the associated isometry subgroup Gq has necessarily three-dimensional non-null orbits

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“…This solution also have been rediscovered later on and we refer to a short remark by Knutsen 10 for further references. 11. 11.…”

Section: Introductionmentioning

confidence: 99%

Scalar fields coupled to gravity in (3+1) dimensions: Static spherically symmetric stiff matter solutions

Bilge¹,

Dağhan²

2007

Journal of Mathematical Physics

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Einstein's field equations for a spherically symmetric metric and a massless scalar field source are reduced to a system effectively of second order in time for the metric function . The solutions of this system split into two classes that we called the positive and negative branches, corresponding to scalar fields with spacelike and timelike gradients. Static solutions for the positive branch are well known, but the proof that = 0 is a global attractor for the region s + Ͼ 0, Ͻ 1 / 2 is given for completeness. The negative branch of static solutions have the interpretation of a perfect fluid with pressure equal to mass density, called "stiff matter." The main result of the paper is the characterization of static solutions of the negative branch by phase plane analysis. We prove that the solution =1/4 is a global attractor for the region where s + Ͼ 0 and Ͻ 1 / 2. Two first integrals, one of which reducing to the solution =1/4 in the static case, are also presented.

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Static spherically symmetric stiff matter in general relativity

Cited by 9 publications

References 8 publications

Relativistic compact objects in isotropic coordinates

Relativistic compact objects in isotropic coordinates

Self-similar static solutions admitting a 2-space of constant curvature

Scalar fields coupled to gravity in (3+1) dimensions: Static spherically symmetric stiff matter solutions

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