Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory

Abstract

We develop a Hamiltonian formalism of brane-world gravity, which singles out two preferred, mutually orthogonal directions. One is a unit twist-free field of spatial vectors with integral lines intersecting perpendicularly the brane. The other is a temporal vector field with respect to which we perform the Arnowitt-Deser-Misner decomposition of the Einstein-Hilbert Lagrangian. The gravitational variables arise from the projections of the spatial metric and their canonically conjugated momenta as tensorial, vectorial and scalar quantities defined on the family of hypersurfaces containing the brane. They represent the gravitons, a gravi-photon and a gravi-scalar, respectively. From the action we derive the canonical evolution equations and the constraints for these gravitational degrees of freedom both on the brane and outside it. By integrating across the brane, the dynamics also generates the tensorial and scalar projection of the Lanczos equation. The vectorial projection of the Lanczos equation arises in a similar way from the diffeomorphism constraint. Both the graviton and the gravi-scalar are continuous across the brane, however the momentum of the gravi-vector has a jump, related to the energy transport (heat flow) on the brane.

13 pages

References in corpus (4)

• The Einstein Equations on the 3-Brane World
• Brane-world gravity
• Generalized Friedmann branes
• Gravitational dynamics in s+1+1 dimensions

Cited by in corpus (21)

• Brane-world stars with solid crust and vacuum exterior
• Thin accretion disks onto brane world black holes
• High Precision Astrometric Millimeter VLBI Using a New Method for Atmospheric Calibration
• Classical tests of general relativity in brane world models
• Jacobi stability of the vacuum in the static spherically symmetric brane world models
• Null fluid collapse in brane world models
• Magnetized Particle Capture Cross Section for Braneworld Black Hole
• The paradox of soft singularity crossing and its resolution by distributional cosmological quantitities
• Effective field theory of modified gravity on the spherically symmetric background: leading order dynamics and the odd-type perturbations
• Quasi-local photon surfaces in general spherically symmetric spacetimes
• Quark-Hadron Phase Transitions in Brane-World Cosmologies
• Inflation and late time acceleration in braneworld cosmological models with varying brane tension
• Covariant gravitational dynamics in 3+1+1 dimensions
• Inflating wormholes in the braneworld models
• Reheating the Universe in Braneworld Cosmological Models with bulk-brane energy transfer
• Plasma Magnetosphere of Rotating Magnetized Neutron Star in the Braneworld
• Weyl fluid dark matter model tested on the galactic scale by weak gravitational lensing
• Minimally coupled scalar fields as imperfect fluids
• Gravitational dynamics in a 2+1+1 decomposed spacetime along nonorthogonal double foliations: Hamiltonian evolution and gauge fixing
• Spherically symmetric, static black holes with scalar hair, and naked singularities in nonminimally coupled k-essence
• Hamiltonian dynamics of doubly-foliable space-times