Narrow Results

The problem of a spherically symmetric charged thin shell of dust collapsing gravitationally into a charged Reissner–Nordström black hole in d space–time dimensions is studied within the theory of general relativity. Static charged shells in such a background are also analyzed. First, a derivation of the equation of motion of such a shell in a d-dimensional space–time is given. Then, a proof of the cosmic censorship conjecture in a charged collapsing framework is presented, and a useful constraint which leads to an upper bound for the rest mass of a charged shell with an empty interior is derived. It is also proved that a shell with total mass equal to charge, i.e. an extremal shell, in an empty interior, can only stay in neutral equilibrium outside its gravitational radius. This implies that it is not possible to generate a regular extremal black hole by placing an extremal dust thin shell within its own gravitational radius. Moreover, it is shown, for an empty interior, that the rest mass of the shell is limited from above. Then, several types of behavior of oscillatory charged shells are studied. In the presence of a horizon, it is shown that an oscillatory shell always enters the horizon and reemerges in a new asymptotically flat region of the extended Reissner–Nordström space–time. On the other hand, for an overcharged interior, i.e. a shell with no horizons, an example showing that the shell can achieve a stable equilibrium position is presented. The results presented have applications in brane scenarios with extra large dimensions, where the creation of tiny higher-dimensional charged black holes in current particle accelerators might be a real possibility, and generalize to higher dimensions previous calculations on the dynamics of charged shells in four dimensions.

We perform quantization of a model in which gravity is coupled to a circular dust shell in $2+1$ spacetime dimensions. Canonical analysis shows that momentum space of this model is $AD{S}^2$-space, and the global chart for it is provided by the Euler angles. In quantum kinematics, this results in non-commutativity in coordinate space and discreteness of the shell radius in timelike region, which includes the collapse point. At the level of quantum dynamics, we find transition amplitudes between zero and non-zero eigenvalues of the shell radius, which describe the rate of gravitational collapse (bounce). Their values are everywhere finite, which could be interpreted as resolution of the central singularity.

In this paper, we studied the dynamics of thin shell in the perfect fluid composed of scalar field. To formulate the equation of motion of the shell, we used the Israel thin-shell formalism for the Brane-world black hole in the two surrounding vacuum regions (interior and exterior). In this study, we considered the potential function as a quadratic function of scalar field. The resulting dynamical equations have been analyzed numerically for both the cases, massless and massive scalar field through the effective potential and radius of the shell by considering different settings of the parameters involved. We found that there are three possibilities in this geometry, thin shell in the scalar field can expand, collapse or attain equilibrium for a while, however, in most of the cases for large value of radius, thin shell collapses to zero size. The effects of the parameters $\alpha$ and $\beta$ (involved due to the Brane-world geometry) on the expansion and collapsing rates have been analyzed and the obtained results compared with the Schwarzschild case ($\alpha =0$, $\beta =0$).

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.

In this paper, a rotating thin shell in a (2 + 1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2 + 1) dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy–density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy–momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the dragging of inertial frames, also occur in rotating (2 + 1)-dimensional spacetimes. The weak and the dominant energy condition for these shells are discussed.

We address the problem of stitching together the vacuum, static, planar-symmetric Taub spacetime and the flat Friedmann–Robertson–Walker (FRW) cosmology using the Israel thin shell formalism. The joining of Taub and FRW spacetimes is reminiscent of the Oppenheimer–Snyder collapse used in modeling the formation of a singularity from a collapsing spherical ball of dust. A possible mechanism for the formation of a planar singularity is provided. It is hoped that tackling such example will improve our intuition on planar-symmetric systems in Einstein’s general relativity (GR).

Using the principle of least action, the motion equations for a singular hypersurface of arbitrary type in quadratic gravity are derived. Equations containing the “external pressure” and the “external flow” components of the surface energy–momentum tensor together with the Lichnerowicz conditions serve to find the hypersurface itself, while the remaining ones define arbitrary functions that arise due to the implicit presence of the delta function derivative. It turns out that neither double layers nor thin shells exist for the quadratic Gauss–Bonnet term. It is shown that there is no “external pressure” for null singular hypersurfaces. The Lichnerowicz conditions imply the continuity of the scalar curvature in the case of spherically symmetric null singular hypersurfaces. These hypersurfaces must be thin shells if the Lichnerowicz conditions are necessary. It is shown that for this particular case the Lichnerowicz conditions can be completely removed therefore a spherically symmetric null double layer exists. Spherically symmetric null singular hypersurfaces in conformal gravity are explored as application.

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.

Presented herein is a formulation for the buckling of a cylindrical shell subjected to external loads using an infinitesimal shell element defined in a convenient coordinate system. The governing equation in terms of the radial deflection is derived for the element by adopting an operator. The eighth order partial differential equation derived can be applied for cylindrical shells with various boundary conditions. For illustration, simply supported cylindrical shells subjected to axial compressive forces are studied using either a one-variable or a two-variable shape function. The critical stresses obtained for the buckling of cylindrical shells are compared with those by the finite element program SAP2000. The critical stress of the cylindrical shell is similar to that of the column, in that the critical stress decreases as the thickness ratio (the ratio of R/h) or the slenderness ratio increases. Good agreement has been obtained for most of the comparative cases, while the finite element results appear to be slightly higher for some cases.

This paper presents a proposed methodology to account for cyclic plastic response of the thin shell ANDES and line-spring finite elements. A through thickness integration scheme is employed for the shell element and stress resultant plasticity is used for the line-spring element. A simplified contact formulation to account for crack closure in the line-spring element is also presented. Numerical comparisons between the proposed models and detailed 3D analyses (pipes) are carried out and presented herein. A comparison between the present implementation and large scale experiment of a surface cracked pipe subjected to large cyclic plastic strains is also presented. The purpose of the presented implementation is to account for cyclic loading in pipeline technology where significant amount of plasticity in the loading cycles occurs.

We describe an example of thin charged shell with equation of state ϵ = τ (Nambu- Goto membrane; τ is tension) that allows a stable configuration such as it exist a region around the shell where gravity has a repulsive behavior. The shell corresponds to a naked Reissner-Nordstrom solution having a charge Q > M, and positive mass M.