Kinematic self-similar plane symmetric solutions

Sharif, M.; Aziz, Sehar

doi:10.1088/0264-9381/24/3/006

Cited by 18 publications

(30 citation statements)

References 24 publications

(72 reference statements)

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“…For the metric (7), there arise three KSS solutions in the tilted perfect fluid case and coincide with the results given by Sintes [25] for n = 0 and m = c in the first, zeroth and second kinds. For the infinite kind, we find three solutions which do not agree with the solutions given in [25].…”

Section: Resultssupporting

confidence: 85%

“…The parallel perfect fluid case gives three independent KSS solutions in the first, zeroth and second kinds. These solutions also coincide with those given in [25]. The infinite kind yields the same solutions as for the tilted perfect fluid case of the infinite kind when c = 0.…”

Section: Resultssupporting

confidence: 82%

“…For the infinite kind, we find three solutions which do not agree with the solutions given in [25]. It is mentioned here that the KSS solutions of the first kind turns out to be the radiation case and the tilted perfect fluid case of the infinite kind reduces to the parallel perfect fluid case for k = ±1.…”

Section: Resultsmentioning

confidence: 55%

“…Recently, Sharif and Sehar [24,25] have explored the KSS solutions of the most general plane symmetric spacetimes. Sintes [26] explored some KSS solutions of locally rotationally symmetric (LRS) spacetimes.…”

Section: Introductionmentioning

confidence: 99%

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Kinematic self-similar solutions of locally rotationally symmetric spacetimes

Sharif¹,

Amir²

2010

Braz. J. Phys.

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This paper contains locally rotationally symmetric kinematic self-similar perfect fluid and dust solutions. We consider three families of metrics which admit kinematic self-similar vectors of the first, second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the orthogonal case gives contradiction both in perfect fluid and dust cases for all the three metrics while the tilted case reduces to the parallel case in both perfect fluid and dust cases for the second metric. The remaining cases give self-similar solutions of different kinds. We obtain a total of seventeen independent solutions out of which two are vacuum. The third metric yields contradiction in all the cases.

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Section: Resultssupporting

confidence: 85%

Section: Resultssupporting

confidence: 82%

Section: Resultsmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Kinematic self-similar solutions of locally rotationally symmetric spacetimes

Sharif¹,

Amir²

2010

Braz. J. Phys.

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“…The third case gives the anti-deSitter universe [24] for A(x) = e 2x = B(x). The last two cases are self similar solutions of infinite Kind for parallel perfect fluid case and dust case [28] when A(x) = 1, B(x) = e 2x and A(x) = x 2 , B(x) = 1 respectively.…”

Section: Killing Symmetries Of Plane Symmetric Spacetimementioning

confidence: 99%

Killing and Noether Symmetries of Plane Symmetric Spacetime

2013

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This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkwoski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub's universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries [1].

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High-speed cylindrical collapse of two perfect fluids

Sharif

Ahmad

2007

Gen Relativ Gravit

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In this paper, the study of the gravitational collapse of cylindrically distributed two perfect fluid system has been carried out. It is assumed that the collapsing speeds of the two fluids are very large. We explore this condition by using the high-speed approximation scheme. There arise two cases, i.e., bounded and vanishing of the ratios of the pressures with densities of two fluids given by c s , d s . It is shown that the high-speed approximation scheme breaks down by non-zero pressures p 1 , p 2 when c s , d s are bounded below by some positive constants. The failure of the high-speed approximation scheme at some particular time of the gravitational collapse suggests the uncertainty on the evolution at and after this time. In the bounded case, the naked singularity formation seems to be impossible for the cylindrical two perfect fluids. For the vanishing case, if a linear equation of state is used, the high-speed collapse does not break down by the effects of the pressures and consequently a naked singularity forms. This work provides the generalisation of the results already given by Nakao and Morisawa (Prog Theor Phys 113:73, 2005) for the perfect fluid.

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Kinematic self-similar plane symmetric solutions

Cited by 18 publications

References 24 publications

Kinematic self-similar solutions of locally rotationally symmetric spacetimes

Kinematic self-similar solutions of locally rotationally symmetric spacetimes

Killing and Noether Symmetries of Plane Symmetric Spacetime

High-speed cylindrical collapse of two perfect fluids

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