0 50 70 63 v 1 1 4 Ju l 2 00 5 Stability analysis of dynamic thin shells (original) (raw)

qc / 0 50 70 63 v 2 6 O ct 2 00 5 Stability analysis of dynamic thin shells

2005

We analyze the stability of generic spherically symmetric thin shells to linearized perturbations around static solutions. We include the momentum flux term in the conservation identity, deduced from the “ADM” constraint and the Lanczos equations. Following the Ishak-Lake analysis, we deduce a master equation which dictates the stable equilibrium configurations. Considering the transparency condition, we study the stability of thin shells around black holes, showing that our analysis is in agreement with previous results. Applying the analysis to traversable wormhole geometries, by considering specific choices for the form function, we deduce stability regions, and find that the latter may be significantly increased by considering appropriate choices for the redshift function. PACS numbers: 04.20.Cv, 04.20.Gz, 04.70.Bw † flobo@cosmo.fis.fc.ul.pt ‡ crawford@cosmo.fis.fc.ul.pt Stability analysis of dynamic thin shells 2

Stability analysis of dynamic thin shells

Classical and Quantum Gravity, 2005

We analyse the stability of generic spherically symmetric thin shells to linearized perturbations around static solutions. We include the momentum flux term in the conservation identity, deduced from the 'ADM' constraint and the Lanczos equations. Following the Ishak-Lake analysis, we deduce a master equation which dictates the stable equilibrium configurations. Considering the transparency condition, we study the stability of thin shells around black holes, showing that our analysis is in agreement with previous results. Applying the analysis to traversable wormhole geometries, by considering specific choices for the form function, we deduce stability regions and find that the latter may be significantly increased by considering appropriate choices for the redshift function.

Stability of transparent spherically symmetric thin shells and wormholes

Physical Review D, 2002

The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the consequences of including the cosmological constant. The approach shows how the existence (or not) of a domain wall dominates the landscape of possible equilibrium configurations.

Linearized stability analysis of thin-shell wormholes with a cosmological constant

Classical and Quantum Gravity, 2004

Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows one to apply a dynamical analysis to the throat, considering linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschildde Sitter solution, the region of stability is significantly increased, relatively to the null cosmological constant case, analyzed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild-anti de Sitter solution, the region of stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for a 0 ≤ 3M the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild-anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild-de Sitter solution, for high values of the cosmological constant and the wormhole throat radius.

Stability Analysis of Thin-Shell Wormholes from Charged Black String

In this paper, we construct thin-shell wormholes from charged black string through cut and paste procedure and investigate its stability. We assume modified generalized Chaplygin gas as a dark energy fluid (exotic matter) present in the thin layer of matter-shell. The stability of these constructed thin-shell wormholes is investigated in the scenario of linear perturbations. We conclude that static stable as well as unstable configurations are possible for cylindrical thin-shell wormholes.

Dynamics of thin-shell wormholes with rotational effects

International Journal of Modern Physics A, 2020

This paper is devoted to the study of the stability of thin-shell wormholes from Kerr black hole. We employ Israel thin-shell formalism to evaluate surface stresses and study the behavior of energy conditions. The linearized stability of rotating thin-shell wormholes is analyzed by taking two different candidates of dark energy as exotic matter at thin-shell. It is found that generalized phantom model ([Formula: see text] which reduces to phantom equation of state as [Formula: see text] and [Formula: see text], where [Formula: see text] is wormhole throat radius and [Formula: see text] is the proper time) yields more stable wormhole solutions as compared to the barotropic equation of state ([Formula: see text], [Formula: see text] is the equation of state parameter and [Formula: see text] is the surface density) for particular ranges of equilibrium throat radius and the whole range of [Formula: see text].

Stability of generic cylindrical thin shell wormholes

Physical Review D, 2014

We revisit the stability analysis of cylindrical thin shell wormholes which have been studied in literature so far. Our approach is more systematic and in parallel to the method which is used in spherically symmetric thin shell wormholes. The stability condition is summarized as the positivity of the second derivative of an effective potential at the equilibrium radius, i.e. V (a0) > 0. This may serve as the master equation in all stability problems for the cylindrical thin-shell wormholes.

New wormhole models with stability analysis via thin-shell in teleparallel gravity

The European Physical Journal C

This study explores new wormhole solutions in the background of teleparallel gravity. All the energy conditions are investigated for two different new calculated shape functions. The presence of exotic matter is confirmed due to the violation of the energy conditions. Thin-shell around the wormhole geometry is obtained by using the cut and paste approach taking the Schwarzschild black hole as an exterior manifold. The stability of thin-shell is explored by using linearized radial perturbation about equilibrium shell radius for both choices of calculated shape functions. It is concluded that stable regions and the position of the expected event horizon depend on the choice of physical parameters.

Linearized Stability of Charged Thin-Shell Wormholes

The linearized stability of charged thin shell wormholes under spherically symmetric perturbations is analyzed. It is shown that the presence of a large value of charge provides stabilization to the system, in the sense that the constraints onto the equation of state are less severe than for non-charged wormholes.

Thin shells around traversable wormholes

Applying the Darmois-Israel thin shell formalism, we construct static and dynamic thin shells around traversable wormholes. Firstly, by applying the cut-and-paste technique we apply a linearized stability analysis to thin-shell wormholes in the presence of a generic cosmological constant. We find that for large positive values of the cosmological constant, i.e., the Schwarzschild-de Sitter solution, the regions of stability significantly increase relatively to the Schwarzschild case, analyzed by Poisson and Visser. Secondly, we construct static thin shell solutions by matching an interior wormhole solution to a vacuum exterior solution at a junction surface. In the spirit of minimizing the usage of exotic matter we analyze the domains in which the weak and null energy conditions are satisfied at the junction surface. The characteristics and several physical properties of the surface stresses are explored, namely, we determine regions where the sign of tangential surface pressure is positive and negative (surface tension). An equation governing the behavior of the radial pressure across the junction surface is deduced. Specific dimensions of the wormhole, namely, the throat radius and the junction interface radius, are found by taking into account the traversability conditions, and estimates for the traversal time and velocity are also determined.