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 Thermodynamical and dynamical stability of a self-gravitating uncharged thin shell

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Santiago Esteban Perez Bergliaffa ◽  
Marcelo Chiapparini ◽  
Luz Marina Reyes
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Thin Shell ◽  
Dynamical Stability ◽  
Thin Shells ◽  
Maximum Mass ◽  
Equilibrium Configurations

Abstract The dynamical stability of massive thin shells with a given equation of state (EOS) (both for the barotropic and non-barotropic case) is here compared with the results coming from thermodynamical stability. Our results show that the restrictions in the para-meter space of equilibrium configurations of the shell following from thermodynamical stability are much more stringent that those obtained from dynamical stability. As a byproduct, we furnish evidence that the link between the maximum mass along a sequence of equilibrium configurations and the onset of dynamical stability is valid for EOS relating the pressure P, the energy density $$\sigma $$σ of the matter on the shell, and its radius R, namely $$P=P(R, \sigma )$$P=P(R,σ).

scholarly journals BAROTROPIC THIN SHELLS WITH LINEAR EOS AS MODELS OF STARS AND CIRCUMSTELLAR SHELLS IN GENERAL RELATIVITY

1999 ◽  
Vol 08 (04) ◽  
pp. 549-555 ◽  
Author(s):  
KONSTANTIN G. ZLOSHCHASTIEV
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Equations Of Motion ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Equilibrium Configurations ◽  
Barotropic Fluids ◽  
Circumstellar Shells ◽  
Relativistic Models ◽  
The Stability

The spherically symmetric thin shells of the barotropic fluids with the linear equation of state are considered within the frameworks of general relativity. We study several aspects of the shells as completely relativistic models of stars, first of all the neutron stars and white dwarfs, and circumstellar shells. The exact equations of motion of the shells are obtained. Also we calculate the parameters of the equilibrium configurations, including the radii of static shells. Finally, we study the stability of the equilibrium shells against radial perturbations.

scholarly journals SINGULAR SHELLS OF QUARK-GLUON MATTER

1999 ◽  
Vol 08 (03) ◽  
pp. 363-371 ◽  
Author(s):  
KONSTANTIN G. ZLOSHCHASTIEV
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Equations Of Motion ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Two Dimensional ◽  
Bag Model ◽  
Equilibrium Configurations

The spherically symmetric thin shells of the macroscopically stable quark-gluon matter are considered within the frameworks of the bag model and theory of discontinuities in general relativity. The equation of state for the two-dimensional matter is suggested, and its features are discussed. The exact equations of motion of such shells are obtained. Distinguishing the two cases, circumstellar and microscopical shells, we calculate the parameters of equilibrium configurations, including the conditions of decay (deconfinement).

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.

Surface Energy Density

2012 ◽  
pp. 2573-2573
Author(s):  
Yimei Zhu ◽  
Hiromi Inada ◽  
Achim Hartschuh ◽  
Li Shi ◽  
Ada Della Pia ◽  
...  
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Surface Energy Density

Surface effect on deformation around an elliptical hole by surface energy density theory

2019 ◽  
Vol 25 (2) ◽  
pp. 337-347
Author(s):  
Liyuan Wang
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Hoop Stress ◽  
Surface Effect ◽  
Plane Deformation ◽  
Surface Elasticity ◽  
Closed Form Solution ◽  
Elliptical Hole ◽  
External Loading ◽  
Surface Energy Density

The finite plane deformation of nanomaterial surrounding an elliptical hole subjected to remote loading is systematically investigated using a recently developed continuum theory. A complex variable formulation is utilized to obtain a closed-form solution for the hoop stress along the edge of the hole. The results show that when the size of the hole reduces to the same order as the ratio of the surface energy density to the applied remote stress, the influence of the surface energy density plays an even more significant role, and the shape of the hole coupled with surface energy density has a significant effect on the elastic state around the hole. Surprisingly, in the absence of any external loading, the hoop stress induced solely by surface effects is identical to that for a hole with surface energy in a linearly elastic solid derived by the Gurtin–Murdoch surface elasticity model. The results in this paper should be useful for the precise design of nanodevices and helpful for the reasonable assessment of test results of nano-instruments.

Size-Dependent Elasticity of Nanoporous Materials Predicted by Surface Energy Density-Based Theory

2017 ◽  
Vol 84 (6) ◽  
Author(s):  
Yin Yao ◽  
Yazheng Yang ◽  
Shaohua Chen
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Volume Fraction ◽  
Surface Effect ◽  
Compressive Strain ◽  
Nanoporous Materials ◽  
Surface Relaxation ◽  
Surface Energy Density ◽  
Closed Form Solutions ◽  
Size Dependent

The size effect of nanoporous materials is generally believed to be caused by the large ratio of surface area to volume, so that it is also called surface effect. Based on a recently developed elastic theory, in which the surface effect of nanomaterials is characterized by the surface energy density, combined with two micromechanical models of composite materials, the surface effect of nanoporous materials is investigated. Closed-form solutions of both the effective bulk modulus and the effective shear one of nanoporous materials are achieved, which are related to the surface energy density of corresponding bulk materials and the surface relaxation parameter of nanomaterials, rather than the surface elastic constants in previous theories. An important finding is that the enhancement of mechanical properties of nanoporous materials mainly results from the compressive strain induced by nanovoid's surface relaxation. With a fixed volume fraction of nanovoids, the smaller the void size, the harder the nanoporous material will be. The results in this paper should give some insights for the design of nanodevices with advanced porous materials or structures.

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.

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