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 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 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 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 Zero-Temperature Equation of State of a Two-Dimensional Bosonic Quantum Fluid with Finite-Range Interaction

2019 ◽  
Vol 4 (1) ◽  
pp. 20 ◽  
Author(s):  
Andrea Tononi
Keyword(s):  
Equation Of State ◽  
Effective Interaction ◽  
Equations Of Motion ◽  
Functional Integration ◽  
Dimensional Regularization ◽  
Two Dimensional ◽  
Finite Range ◽  
Zero Temperature ◽  
Range Interaction ◽  
Dimensional Equation

We derive the two-dimensional equation of state for a bosonic system of ultracold atoms interacting with a finite-range effective interaction. Within a functional integration approach, we employ a hydrodynamic parameterization of the bosonic field to calculate the superfluid equations of motion and the zero-temperature pressure. The ultraviolet divergences, naturally arising from the finite-range interaction, are regularized with an improved dimensional regularization technique.

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 Stability Against Radial Perturbations of Slowly Rotating Neutron Stars

1981 ◽  
Vol 93 ◽  
pp. 327-327
Author(s):  
Kenzo Arai ◽  
Keisuke Kaminishi
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Angular Velocity ◽  
Neutron Stars ◽  
Radial Displacement ◽  
Cold Neutron ◽  
Symmetric Body ◽  
Slow Rotation ◽  
Spherically Symmetric ◽  
Dynamical Equations

The dynamical equations governing pulsation in rotating neutron stars are derived in the framework of general relativity. Stellar models are constructed by using a realistic equation of state for cold neutron matter. Small radial displacement and slow rotation are treated as perturbations on spherically symmetric body. In these models the maximum masses are 1.761 M⊙ at the central density 3.461 × 1015 g cm−3 for a sequence of nonrotating configurations and 2.165 M⊙ for rotating models with the critical angular velocity (GM/R3)½.

scholarly journals Enhanced models for the nonlinear bending of planar rods: localization phenomena and multistability

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200455
Author(s):  
Matteo Brunetti ◽  
Antonino Favata ◽  
Stefano Vidoli
Keyword(s):  
Dimensional Reduction ◽  
Compatibility Condition ◽  
Stable Equilibrium ◽  
Thin Shells ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Nonlinear Bending ◽  
One Dimensional ◽  
Equilibrium Configurations ◽  
Dimensional Models

We deduce a one-dimensional model of elastic planar rods starting from the Föppl–von Kármán model of thin shells. Such model is enhanced by additional kinematical descriptors that keep explicit track of the compatibility condition requested in the two-dimensional parent continuum, that in the standard rods models are identically satisfied after the dimensional reduction. An inextensible model is also proposed, starting from the nonlinear Koiter model of inextensible shells. These enhanced models describe the nonlinear planar bending of rods and allow to account for some phenomena of preeminent importance even in one-dimensional bodies, such as formation of singularities and localization (d-cones), otherwise inaccessible by the classical one-dimensional models. Moreover, the effects of the compatibility translate into the possibility to obtain multiple stable equilibrium configurations.

Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Gas Dynamics ◽  
Hydrodynamic Type ◽  
System Of Equations ◽  
Two Dimensional ◽  
Equations Of Gas Dynamics ◽  
Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

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