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

Abstract

We 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.

21 pages, 3 figures, accepted for publication in PRD

References in corpus (11)

• The virial theorem and the dynamics of clusters of galaxies in the brane world models
• Brane-world cosmology with black strings
• Lookback time as a test for brane cosmology
• Galactic dark matter as a bulk effect on the brane
• On the existence and dynamics of braneworld black holes
• Solar system tests of brane world models
• Spherically symmetric problem on the brane and galactic rotation curves
• Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory
• The luminosity-redshift relation in brane-worlds: I. Analytical results
• The luminosity-redshift relation in brane-worlds: II. Confrontation with experimental data
• Static exteriors for nonstatic braneworld stars

Cited by in corpus (8)

• Thin accretion disks onto brane world black holes
• Gravitational Effects of Rotating Braneworld Black Holes
• Black hole solutions in the quadratic Weyl conformal geometric theory of gravity
• Quark-Hadron Phase Transitions in Brane-World Cosmologies
• Inflation and late time acceleration in braneworld cosmological models with varying brane tension
• Jacobi stability analysis of scalar field models with minimal coupling to gravity in a cosmological background
• Geometry and stability of dynamical systems
• Stability analysis of circular orbits around a traversable wormhole with massless conformally coupled scalar field