Jacobi stability of the vacuum in the static spherically symmetric brane world models

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dc.creatorHarko, T.
dc.creatorSabau, V. S.
dc.date2008-03-31
dc.date2008-05-03
dc.date.accessioned2026-07-07T11:33:25Z
dc.date.available2026-07-07T11:33:25Z
dc.descriptionWe analyze the stability of the structure equations of the vacuum in the brane world models, by using both the linear (Lyapunov) stability analysis, and the Jacobi stability analysis, the Kosambi-Cartan-Chern (KCC) theory. In the brane world models the four dimensional effective Einstein equations acquire extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the 3-brane in the bulk. Generally, the spherically symmetric vacuum solutions of the brane gravitational field equations, have properties quite distinct as compared to the standard black hole solutions of general relativity. We close the structure equations by assuming a simple linear equation of state for the dark pressure. In this case the vacuum is Jacobi stable only for a small range of values of the proportionality constant relating the dark pressure and the dark radiation. The unstable trajectories on the brane behave chaotically, in the sense that after a finite radial distance it would be impossible to distinguish the trajectories that were very near each other at an initial point. Hence the Jacobi stability analysis offers a powerful method for constraining the physical properties of the vacuum on the brane.
dc.description21 pages, 3 figures, accepted for publication in PRD
dc.identifierhttps://arxiv.org/abs/0803.4369
dc.identifierhttp://arxiv.org/abs/0803.4369
dc.identifierPhys.Rev.D77:104009,2008
dc.identifierdoi:10.1103/PhysRevD.77.104009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/197886
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleJacobi stability of the vacuum in the static spherically symmetric brane world models
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