Covariant approach of perturbations in Lovelock type brane gravity

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 Φ . 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 Φ possessing a tachyonic mass. This shows that, to some extent, these types 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.