On the evolution of dust shells in Lemaître-Tolman-Bondi models

Capozziello

Int. J. Geom. Methods Mod. Phys.

2011

Section: λ Is Positive and ε Is Positive Or Nullmentioning

confidence: 99%

THE WEIERSTRASS CRITERION AND THE LEMAÎTRE–TOLMAN–BONDI MODELS WITH COSMOLOGICAL CONSTANT Λ

Capozziello

Int. J. Geom. Methods Mod. Phys.

2011

“…More precisely, in [5,6] the intrinsic geometric properties of the generic initial spatial manifold V 3 were analyzed with particular reference to its Ricci principal curvatures ω 1 , ω 2 , ω 3 ; moreover, it was studied how the curvature of the generic initial spatial hypersurface influences the subsequent evolution of the continuum material. Furthermore, the exact solutions of the main evolution equation in implicit and parametric form in order to stress the role of ω 1 were proposed.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, after examining the general space-time structure and Einstein's equations, we have recalled their evolution equations, called Tolman-Bondi equations. Hence, following[1,2,23] and extending ideas already contained in[3][4][5][6], we have considered a Riemannian manifold M which is topologically…”

mentioning

confidence: 99%

A Review on the Geometric Formulation of Tolman–bondi Equations in General Relativity

Francaviglia

Int. J. Geom. Methods Mod. Phys.

2009

This work is focused on spherically symmetric space-times. More precisely, geometric and structural properties of spatially spherical shells of a dust universe are analyzed in detail considering recent results of our research. Moreover, exact solutions, obtained for constant Ricci principal curvatures, are inferred and qualitatively analyzed through suitable classic analogies.Any physical theory is based partly on a space-time structure, which is needed to locate events (space-time points) and to provide a domain of definition for variables describing particles and field.Hence, we begin by recalling the Riemannian space-time of General Relativity in order to introduce Einstein's equations under the hypothesis of a spherically symmetric space-time. Space-time structure and Einstein equationsIn Einstein's general theory of relativity, space-time is represented mathematically as a pair (M, g) where M is a connected four-dimensional, Hausdorff C ∞ manifold and g is a Lorentzian metric (i.e. a metric of signature +2) on M. The manifold Int. J. Geom. Methods Mod. Phys. 2009.06:595-617. Downloaded from www.worldscientific.com by UNIVERSITY OF AUCKLAND LIBRARY -SERIALS UNIT on 06/10/15. For personal use only. A Review on the Geometric Formulation of T-B Equations 597M is assumed to be connected since we would have no classical knowledge of any disconnected components. It is taken to be Hausdorff since this seems to agree with normal experience. Together with the existence of a Lorentz metric the Hausdorff condition implies that M is paracompact [8,9]. The Lorentzian signature of the metric tensor field g implies that at each point of M the set {X | g(X, X) = 0} of null vectors is a cone in the tangent space. This null cone separates the tangent space into three open parts: the set of futuredirected timelike vectors, that of the past-directed timelike vectors and that of the spacelike vectors.With any kind of matter or radiation there is associated a second rank tensor field T, called energy momentum tensor, which describes the distribution of energy, momentum and stress. It is also assumed that the curvature associated with the metric g is related to matter by Einstein's field equation

Intra-Galactic Thin Shell Wormhole and Its Stability

2013

Int J Theor Phys

In this paper, we construct an intra-galactic thin shell wormhole joining two copies of identical galactic space times described by the Mannheim-Kazanas de Sitter solution in conformal gravity and study its stability under spherical perturbations. We assume the thin shell material as a Chaplygin gas and discuss in detail the values of the relevant parameters under which the wormhole is stable. We study the stability following the method by Eiroa and we also qualitatively analyze the dynamics through the method of Weierstrass. We find that the wormhole is generally unstable but there is a small interval in radius for which the wormhole is stable.