Covariant approach of perturbations in Lovelock type brane gravity

Abstract

We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type extended objects propagating in a flat Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field $\Phi$. Whithin this framework, we analyse the stability of membranes with a de Sitter geometry where we find that the Jacobi equation specializes to a Klein-Gordon (KG) equation for $\Phi$ possessing a tachyonic mass. This shows that, to some extent, these type of extended objects share the symmetries of the Dirac-Nambu-Goto (DNG) action which is by no means coincidental because the DNG model is the simplest included in this type of gravity.

13 pages, 3 figures. Revised version. References updated. Published in Class. Quantum Grav

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Cited by in corpus (7)

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• Hamilton-Jacobi approach for linearly acceleration-dependent Lagrangians
• Holographic relationships in Lovelock type brane gravity
• Lovelock type brane gravity from a minimal surface perspective
• Covariant higher order perturbations of branes in curved spacetime
• Jacobi equations of geodetic brane gravity
• Pulsating string solution and stability in two parameter $\chi$-deformed background