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Register a new userTopological and Geometrical Properties of Brane-Worlds
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Authors
Edmundo M. Monte
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We study the geometrical and topological properties of the bulk (environment space) when we modify the geometry or topology of a brane-world. Through the characterization of a spherically symmetric space-time as a local brane-world immersed into six dimensional pseudo-Euclidean spaces, with different signatures of the bulk, we investigate the existence of a topological difference in the immersed brane-world. In particular the Schwarzschilds brane-world and its Kruskal (or Fronsdal) brane-world extension are examined from point of view of the immersion formalism. We prove that there is a change of signature of the bulk when we consider a local isometric immersion and different topologies of a brane-world in that bulk.
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The topological structure of Schwarzschilds space-time and its maximal analytic extension are investigated in context of brane-worlds. Using the embedding coordinates, these geometries are seen as different states of the evolution of a single brane-world. Comparing the topologies and the embeddings it is shown that this evolution must be followed by a signature change in the bulk.
This paper is dedicated to revisit the modifications caused by branes in the collapse of a stellar structure under the Snyder-Oppenheimer scheme. Due to the homogeneity and isotropy of the model, we choose study the case of a closed geometry described by $k=1$, through the tool of dynamical systems. We revisit the different components of the star and its evolution during the stellar collapse, paying particular attention to the non-local effects and the quadratic terms of the energy momentum tensor that come from branes corrections. In the same vein we realize a phase portrait together with a stability analysis with the aim of obtain information about the attractors or saddle points of the dynamical system under different initial conditions in the density parameters, remarking the parameters that come from branes contributions.
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Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise, is appropriate for a broader spectrum of audiences ranging from students to researchers, thus illustrations of differential forms and relevant basic topological concepts are also offered, followed by the demonstration with formulation of differential forms of the classical Navier-Stokes flow theory and the discussions of recent studies in fundamental fluid mechanics and turbulence.
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