scholarly journals KINEMATIC SELF-SIMILAR CYLINDRICALLY SYMMETRIC SOLUTIONS

2005 ◽  
Vol 14 (09) ◽  
pp. 1527-1543 ◽  
Author(s):  
M. SHARIF ◽  
SEHAR AZIZ
Keyword(s):  
Perfect Fluid ◽  
Vacuum Solution ◽  
Cylindrically Symmetric ◽  
Self Similar ◽  
Parallel Case ◽  
Dust Case

This paper is devoted to find out cylindrically symmetric kinematic self-similar perfect fluid and dust solutions. We study the cylindrically symmetric solutions which admit kinematic self-similar vectors of 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 parallel case gives contradiction both in the perfect fluid and dust cases. The orthogonal perfect fluid case yields a vacuum solution while the orthogonal dust case gives contradiction. It is worth mentioning that the tilted case provides solution both for the perfect as well as dust cases.

scholarly journals A type of Levi–Civita solution in modified Gauss–Bonnet gravity

2014 ◽  
Vol 92 (2) ◽  
pp. 173-176 ◽  
Author(s):  
M.E. Rodrigues ◽  
M.J.S. Houndjo ◽  
D. Momeni ◽  
R. Myrzakulov
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Perfect Fluid ◽  
Cosmic String ◽  
Coupling Parameter ◽  
Vacuum Solution ◽  
Einstein Gravity ◽  
Parameter Family ◽  
Bonnet Gravity ◽  
Cylindrically Symmetric

Herein we obtain an exact solution for cylindrically symmetric modified Gauss–Bonnet gravity. This metric is a generalization of the vacuum solution of Levi–Civita in general relativity. It describes an isotropic perfect fluid one-parameter family of the gravitational configurations, which can be interpreted as the exterior metric of a cosmic string. By setting the Gauss–Bonnet coupling parameter to zero, we recover the vacuum solution in the Einstein gravity as well.

scholarly journals Gravitational binding energy in charged cylindrical symmetry

2012 ◽  
Vol 90 (12) ◽  
pp. 1233-1236 ◽  
Author(s):  
M. Sharif ◽  
M. Zaeem Ul Haq Bhatti
Keyword(s):  
Binding Energy ◽  
Perfect Fluid ◽  
Mass Function ◽  
Cylindrical Symmetry ◽  
Electric Coupling ◽  
Cylindrically Symmetric

We consider a static, cylindrically symmetric, charged, gravitating object as a perfect fluid and investigate the gravitational binding energy. It is found that only the localized part of the mass function provides the gravitational binding energy, whereas the nonlocalized part generated by the electric coupling does not contribute to it.

Cylindrical shock and detonation waves in magnetogasdynamics

1969 ◽  
Vol 39 (4) ◽  
pp. 705-725 ◽  
Author(s):  
A. H. Christer ◽  
J. B. Helliwell
Keyword(s):  
Shock Waves ◽  
Strong Shock ◽  
Flow Patterns ◽  
Detonation Waves ◽  
Cylindrically Symmetric ◽  
Constant Strength ◽  
Self Similar ◽  
Axis Of Symmetry ◽  
Similar Solutions ◽  
Shock And Detonation Waves

Self-similar flow patterns are studied which arise when a cylindrically symmetric strong shock or detonation wave propagates outwards into a gas at rest in which the ambient density varies as the inverse square of the distance from the axis of symmetry along which flows a line current of either zero or finite constant strength. The electrical conductivity of the gas on either side of the wave is supposed perfect and the discontinuities discussed are either gasdynamic or magnetogas-dynamic in nature. It is shown that self-similar solutions exist for piston driven gasdynamic detonation and shock waves. Whilst no self-similar solutions may occur for magnetogasdynamic detonation waves, it is demonstrated that magnetogasdynamic shock waves do possess such solutions for which detailed flow patterns are presented.

scholarly journals STATIC CYLINDRICALLY SYMMETRIC INTERIOR SOLUTIONS IN f(R) GRAVITY

2012 ◽  
Vol 27 (25) ◽  
pp. 1250138 ◽  
Author(s):  
M. SHARIF ◽  
SADIA ARIF
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Functional Form ◽  
Ricci Scalar ◽  
The Other ◽  
New Exact Solutions ◽  
Cylindrically Symmetric ◽  
Theory Of Gravity ◽  
Interior Solutions

We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric f(R) theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of f(R). It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in f(R) gravity.

scholarly journals The Kasner brane

2015 ◽  
Vol 30 (34) ◽  
pp. 1550185
Author(s):  
Mark D. Roberts
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Vacuum Solution ◽  
Energy Conditions ◽  
Field Equations ◽  
Einstein Tensor ◽  
Five Dimensions

Solutions are found to field equations constructed from the Pauli, Bach and Gauss–Bonnet quadratic tensors to the Kasner and Kasner brane spacetimes in up to five dimensions. A double Kasner space is shown to have a vacuum solution. Brane solutions in which the bulk components of the Einstein tensor vanish are also looked at and for four-branes a solution similar to radiation Robertson–Walker spacetime is found. Matter trapping of a test scalar field and a test perfect fluid are investigated using energy conditions.

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