Jacobi equations of geodetic brane gravity
arXiv:2202.13035 · doi:10.1088/1361-6382/ac9a31
Abstract
We consider brane gravity as described by the Regge-Teitelboim geometric model, in any codimension. In brane gravity our spacetime is modeled as the time-like world volume spanned by a space-like brane in its evolution, seen as a manifold embedded in an ambient background Minkowski spacetime of higher dimension. Although the equations of motion of the model are well known, apparently their linearization has not been considered before. Using a direct approach, we linearize the equations of motion about a solution, obtaining the Jacobi equations of the Regge- Teitelboim model. They take a formidable aspect. Some of their features are commented upon. By identifying the Jacobi equations, we derive an explicit expression for the Morse index of the model. To be concrete, we apply the Jacobi equations to the study of the stability of a four-dimensional Schwarzschild spacetime embedded in a six-dimensional Minkowski spacetime. We find that it is unstable under small linear deformations.
References in corpus (33)
- A Large Mass Hierarchy from a Small Extra Dimension
- The Hierarchy Problem and New Dimensions at a Millimeter
- Dynamics of dark energy
- f(R) Theories Of Gravity
- Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
- A History of Dark Matter
- Black Strings and p-Branes are Unstable
- Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
- Brane-World Gravity
- Brane-World Black Holes
- Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric
- Advanced Methods in Black-Hole Perturbation Theory
- Interferometer Techniques for Gravitational-Wave Detection
- Geometry of Deformations of Relativistic Membranes
- Evolution of cosmological perturbations in a brane-universe
- General Embedded Brane Effective Field Theories
- Geodetic Brane Gravity
- Perturbations of brane worlds
- Curvature Corrections to Dynamics of Domain Walls
- Cosmological perturbations in the DGP braneworld: numeric solution
- An Alternative to Matter Localization in the "Brane World": An Early Proposal and its Later Improvements
- Covariant perturbations of domain walls in curved spacetime
- Quantum Gravity of a Brane-like Universe
- Embeddings for Schwarzschild metric: classification and new results
- Born-Infeld extension of Lovelock brane gravity
- A new approach to the study of quasi-normal modes of rotating stars
- Late time cosmic acceleration in modified Sáez-Ballester theory
- Non-relativistic limit of embedding gravity as General Relativity with dark matter
- Geodesic deviation in Saez--Ballester theory
- Multiple-scales analysis of cosmological perturbations in brane-worlds
- Covariant approach of perturbations in Lovelock type brane gravity
- Cosmic acceleration in Regge-Teitelboim gravity
- Friedmann cosmology in Regge-Teitelboim gravity