ON THE DYNAMICS OF A CLASS OF EINSTEIN–VLASOV SHELLS

2011 ◽  
Vol 20 (05) ◽  
pp. 661-674
Author(s):  
REINALDO J. GLEISER ◽  
MARCOS A. RAMIREZ
Keyword(s):  
Angular Momentum ◽  
Thin Shell ◽  
Continuous Distribution ◽  
Related Result ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Vlasov Equations ◽  
Finite Set ◽  
Thick Shells ◽  
Symmetric Systems

The Einstein–Vlasov equations govern the dynamics of systems of self-gravitating collisionless particles in the framework of general relativity. Here we review some recent results obtained by restricting to spherically symmetric systems and imposing the simplifying restrictions that the conserved angular momentum of the particles can take values only on a discrete, finite set. The first set of results is restricted to the existence of thin shells, their dynamics and stability. A second set is concerned with the existence of thick shells satisfying the same restrictions and the conditions under which they admit, in general, a thin shell limit. In a related result it is shown that the so called Einstein shells have a unique thin shell limit where the particle's angular momentum has a continuous distribution.

scholarly journals Stability of spherically symmetric timelike thin-shells in general relativity with a variable equation-of-state

2017 ◽  
Vol 26 (14) ◽  
pp. 1750158 ◽  
Author(s):  
S. Habib Mazharimousavi ◽  
M. Halilsoy ◽  
S. N. Hamad Amen
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Energy Density ◽  
Surface Energy ◽  
Thin Shell ◽  
Minkowski Spacetime ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Surface Energy Density ◽  
Variable Equation

We study spherically symmetric timelike thin-shells in [Formula: see text]-dimensional bulk spacetime with a variable equation-of-state for the fluid presented on the shell. In such a fluid, the angular pressure [Formula: see text] is a function of both surface energy density [Formula: see text] and the radius [Formula: see text] of the thin-shell. Explicit cases of the thin shells connecting two nonidentical cloud of strings spacetimes and a flat Minkowski spacetime to the Schwarzschild metric are investigated.

scholarly journals TRAVERSABLE WORMHOLES IN A STRING CLOUD

2008 ◽  
Vol 17 (08) ◽  
pp. 1179-1196 ◽  
Author(s):  
MARTÍN G. RICHARTE ◽  
CLAUDIO SIMEONE
Keyword(s):  
Thin Shell ◽  
Dimensional Space ◽  
Space Time ◽  
Exotic Matter ◽  
Spherically Symmetric ◽  
Related Model ◽  
Traversable Wormholes ◽  
Dimensional Space Time ◽  
Thin Shell Wormholes ◽  
The Stability

We study spherically symmetric thin shell wormholes in a string cloud background in (3 + 1)-dimensional space–time. The amount of exotic matter required for the construction, the traversability and the stability of such wormholes under radial perturbations are analyzed as functions of the parameters of the model. In addition, in the appendices a nonperturbative approach to the dynamics and a possible extension of the analysis to a related model are briefly discussed.

scholarly journals The theory of spherically symmetric thin shells in conformal gravity

2018 ◽  
Vol 27 (06) ◽  
pp. 1841012 ◽  
Author(s):  
Victor Berezin ◽  
Vyacheslav Dokuchaev ◽  
Yury Eroshenko
Keyword(s):  
General Relativity ◽  
Weyl Tensor ◽  
Delta Function ◽  
Einstein Gravity ◽  
Riemann Tensor ◽  
Momentum Tensor ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Gravitational Fields ◽  
Gravitational Theories

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy–momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl–Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ([Formula: see text] massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl–Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

scholarly journals Minimal Length Effects on Tunnelling from Spherically Symmetric Black Holes

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Benrong Mu ◽  
Peng Wang ◽  
Haitang Yang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Minimal Length ◽  
Jacobi Method ◽  
Spherically Symmetric ◽  
Infinite Time ◽  
Quantum Tunnelling ◽  
Zero Mass ◽  
Jacobi Equations

We investigate effects of the minimal length on quantum tunnelling from spherically symmetric black holes using the Hamilton-Jacobi method incorporating the minimal length. We first derive the deformed Hamilton-Jacobi equations for scalars and fermions, both of which have the same expressions. The minimal length correction to the Hawking temperature is found to depend on the black hole’s mass and the mass and angular momentum of emitted particles. Finally, we calculate a Schwarzschild black hole's luminosity and find the black hole evaporates to zero mass in infinite time.

On the Dynamic Stability of Fluid-Conveying Pipes

1973 ◽  
Vol 40 (1) ◽  
pp. 48-52 ◽  
Author(s):  
D. S. Weaver ◽  
T. E. Unny
Keyword(s):  
Potential Theory ◽  
Dynamic Stability ◽  
Thin Shell ◽  
Critical Flow ◽  
Thin Shells ◽  
Classical Potential ◽  
Classical Potential Theory ◽  
Limiting Case ◽  
Beam Mode ◽  
Fluid Conveying Pipes

This paper presents a general analysis of the dynamic stability of a finite-length, fluid-conveying pipe. The Flu¨gge-Kempner equation is used in conjunction with classical potential theory so that circumferential modes as well as the usual beam modes may be considered. The cylinders are found to become unstable statically at first but flutter is predicted for higher velocities. The critical flow velocities for short, thin shells are associated with a number of circumferential waves. This number reduces for thicker and longer shells until the instability is in a beam mode. When the limiting case of a long thin shell is taken, it is found to agree with previous results obtained using a simpler beam approach.

scholarly journals Evolution of thin shells in D-dimensional general relativity

2019 ◽  
Vol 28 (04) ◽  
pp. 1950069 ◽  
Author(s):  
Marcos A. Ramirez ◽  
Daniel Aparicio
Keyword(s):  
Energy Condition ◽  
Cosmic Censorship ◽  
Einstein Equations ◽  
Thin Shells ◽  
Dominant Energy Condition ◽  
Spherically Symmetric ◽  
Barotropic Fluids ◽  
Large Shell ◽  
Asymptotic Dynamics ◽  
Electrovacuum Solution

In this paper, we consider singular timelike spherical hypersurfaces embedded in a [Formula: see text]-dimensional spherically symmetric bulk spacetime which is an electrovacuum solution of Einstein equations with cosmological constant. We analyze the different possibilities regarding the orientation of the gradient of the standard [Formula: see text] coordinate in relation to the shell. Then we study the dynamics according to Einstein equations for arbitrary matter satisfying the dominant energy condition. In particular, we thoroughly analyze the asymptotic dynamics for both the small and large-shell-radius limits. We also study the main qualitative aspects of the dynamics of shells made of linear barotropic fluids that satisfy the dominant energy condition. Finally, we prove weak cosmic censorship for this class of solutions.

Vibration of Shallow Shells: A Review With Bibliography

1997 ◽  
Vol 50 (8) ◽  
pp. 431-444 ◽  
Author(s):  
K. M. Liew ◽  
C. W. Lim ◽  
S. Kitipornchai
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Free Vibration Analysis ◽  
Review Article ◽  
Shallow Shells ◽  
First Order ◽  
Recent Developments ◽  
Thick Shells ◽  
Thin Shell Theory ◽  
Introductory Review

This review article documents recent developments in the free vibration analysis of thin, moderately thick, and thick shallow shells. An introductory review of the studies in Kirchhoff-Love classical thin shell theory is given. The development of studies in moderately thick shells incorporating the effects of transverse shear deformation and rotary inertia is detailed. This review article mainly focuses on research advances in vibration studies since the 1970s using the classical Kirchhoff-Love, first-order, and higher-order theories. The validity and range of applicability of these theories are examined. There are 163 references listed at the end of the article.

scholarly journals Approximation of Linear Elastic Shells by Curved Triangular Finite Elements Based on Elastic Thick Shells Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Joseph Nkongho Anyi ◽  
Robert Nzengwa ◽  
Jean Chills Amba ◽  
Claude Valery Abbe Ngayihi
Keyword(s):  
Thin Shell ◽  
Thick Shell ◽  
Absolute Value ◽  
Linear Elastic ◽  
Limit Value ◽  
Shell Equations ◽  
Third Fundamental Form ◽  
Nodal Displacements ◽  
Thick Shells ◽  
Thin Shell Theory

We have developed a curved finite element for a cylindrical thick shell based on the thick shell equations established in 1999 by Nzengwa and Tagne (N-T). The displacement field of the shell is interpolated from nodal displacements only and strains assumption. Numerical results on a cylindrical thin shell are compared with those of other well-known benchmarks with satisfaction. Convergence is rapidly obtained with very few elements. A scaling was processed on the cylindrical thin shell by increasing the ratioχ=h/2R(half the thickness over the smallest radius in absolute value) and comparing results with those obtained with the classical Kirchhoff-Love thin shell theory; it appears that results diverge at2χ=1/10=0.316because of the significant energy contribution of the change of the third fundamental form found in N-T model. This limit value of the thickness ratio which characterizes the limit between thin and thick cylindrical shells differs from the ratio 0.4 proposed by Leissa and 0.5 proposed by Narita and Leissa.

Spherically symmetric thin shells in Brans-Dicke theory of gravity

1993 ◽  
Vol 48 (2) ◽  
pp. 631-646 ◽  
Author(s):  
Patricio S. Letelier ◽  
Anzhong Wang
Keyword(s):  
Thin Shells ◽  
Spherically Symmetric ◽  
Theory Of Gravity
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