scholarly journals General solutions of Einstein’s spherically symmetric gravitational equations with junction conditions

2003 ◽  
Vol 44 (12) ◽  
pp. 5637 ◽  
Author(s):  
A. Das ◽  
A. DeBenedictis ◽  
N. Tariq
Keyword(s):  
Spherically Symmetric ◽  
Junction Conditions ◽  
General Solutions ◽  
Gravitational Equations

Five-dimensional spherical gravitational collapse of anisotropic fluid with cosmological constant

2017 ◽  
Vol 14 (02) ◽  
pp. 1750025 ◽  
Author(s):  
Suhail Khan ◽  
Hassan Shah ◽  
Ghulam Abbas
Keyword(s):  
Cosmological Constant ◽  
Apparent Horizon ◽  
Physical Significance ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Hole Size ◽  
Junction Conditions ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Exterior Regions

Our aim is to study five-dimensional spherically symmetric anisotropic collapse with a positive cosmological constant (PCC). For this purpose, five-dimensional spherically symmetric and Schwarzschild–de Sitter metrics are chosen in the interior and exterior regions respectively. A set of junction conditions is derived for the smooth matching of interior and exterior spacetimes. The apparent horizon is calculated and its physical significance is studied. It comes out that the whole collapsing process is influenced by the cosmological constant. The collapsing process under the influence of cosmological constant slows down and black hole size also reduced.

scholarly journals EXPANSIONFREE FLUID EVOLUTION AND SKRIPKIN MODEL IN f(R) THEORY

2011 ◽  
Vol 20 (11) ◽  
pp. 2239-2252 ◽  
Author(s):  
M. SHARIF ◽  
H. RIZWANA KAUSAR
Keyword(s):  
General Relativity ◽  
The Self ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Dynamical Equations ◽  
Constant Energy ◽  
Isotropic Pressure ◽  
Symmetric Star ◽  
Constant Energy Density ◽  
General Influence

We consider the modified f(R) theory of gravity whose higher-order curvature terms are interpreted as a gravitational fluid or dark source. The gravitational collapse of a spherically symmetric star, made up of locally anisotropic viscous fluid, is studied under the general influence of the curvature fluid. Dynamical equations and junction conditions are modified in the context of f(R) dark energy and by taking into account the expansionfree evolution of the self-gravitating fluid. As a particular example, the Skripkin model is investigated which corresponds to isotropic pressure with constant energy density. The results are compared with corresponding results in General Relativity.

Discontinuities in spherically symmetric gravitational fields and shells of radiation

1958 ◽  
Vol 248 (1254) ◽  
pp. 404-414 ◽  
Keyword(s):  
Boundary Conditions ◽  
Spherical Shell ◽  
Previous Treatment ◽  
Empty Space ◽  
Point Of View ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Metric Tensor ◽  
Gravitational Fields

Boundary conditions at a 3-space of discontinuity ∑ are considered from the point of view of Lichnerowicz. The validity of the O’Brien—Synge junction conditions is established for co-ordinates derivable from Lichnerowicz’s ‘admissible co-ordinates’ by a transformation which is uniformly differentiable across ∑. The co-ordinates r , θ , ϕ , t , used by Schwarzschild and most later authors when dealing with spherically symmetric fields, are shown to be of this type. In Schwarzschild’s co-ordinates, the components of the metric tensor can always be made continuous across Ʃ, and simple relations are derived connecting the jumps in their first derivatives. A spherical shell of radiation expanding in empty space is examined in the light of the above ideas, and difficulties encountered by Raychaudhuri in a previous treatment of this problem are cleared up. A particular model is then discussed in some detail.

scholarly journals A general solution of Einstein's Equations for systems involving three variables

1930 ◽  
Vol 128 (808) ◽  
pp. 523-530
Keyword(s):  
General Solution ◽  
Boundary Conditions ◽  
Physical Interpretation ◽  
Empty Space ◽  
Riemann Tensor ◽  
Successive Approximations ◽  
General Solutions ◽  
Exponential Factors ◽  
Time Variables ◽  
Gravitational Equations

§ 1. In this paper we produce and discuss some general solutions of Einstein’s gravitational equations. For simplicity we restrict the group of solutions to those which involve only three of the space-time variables explicitly. It is immaterial which co-ordinate does not occur explicitly as we can, by transformation and appropriate boundary conditions, choose this co-ordinate to be whichever is desired. The transformation may be an imaginary one, but in the analysis no reality conditions are implied, so that choice of the time co-ordinate is purely a matter of the physical interpretation of the final results. We consider first the Cartesian ground-form in completely empty space, and modify it by the introduction of exponential factors, thus ds 2 = — e ­ λ dx 2 — e μ dy 2 — e γ dz 2 + e ρ dt 2 , where λ, μ, γ, ρ are to be explicit functions of ( x, y, z ). This ground-form is to be thought of as a Cartesian ground-form in empty space which has been perturbed by the presence of the non-vanishing functions λ, μ, γ, ρ and we endeavour to interpret this perturbation as the result of the introduction of matter into the previously empty world. This interpretation may be permissible provided the components of the contracted Riemann tensor G μγ , vanish at all points unoccupied by matter, and that the necessary boundary conditions and continuity also obtain. These equations G μγ = 0 are then solved for λ, μ, γ, ρ. By regarding λ, μ, γ, ρ as perturbations it is not unreasonable to attempt to solve the gravitational equations, by a series of successive approximations, to be determined by selecting the terms in succession, according to their weight in λ, μ, γ, ρ.

scholarly journals SPHERICALLY SYMMETRIC THICK BRANES IN VACUUM

2004 ◽  
Vol 19 (27) ◽  
pp. 4687-4694 ◽  
Author(s):  
MASSOUD BORHANI ◽  
REZA MANSOURI ◽  
SAMAD KHAKSHOURNIA
Keyword(s):  
Finite Thickness ◽  
Equation Of Motion ◽  
Space Time ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Bulk Space ◽  
Thick Branes

We consider a spherical thick 3-brane immersed in a five-dimensional bulk space–time. We demonstrate how the thick brane equation of motion expanded in powers of the thickness of the brane can be obtained from the expected junction conditions on the boundaries of thick brane with the two embedding space–times. It is shown that the finite thickness corrections lead to a faster collapse of the brane in the vacuum.

Junction conditions on null hypersurfaces for spherically symmetric metrics

1991 ◽  
Vol 32 (6) ◽  
pp. 1537-1540
Author(s):  
Zu‐hui Fan ◽  
Zhi‐quan Kuang ◽  
Can‐bin Liang ◽  
Yun‐qiang Yu
Keyword(s):  
Spherically Symmetric ◽  
Junction Conditions ◽  
Null Hypersurfaces ◽  
Symmetric Metrics
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