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

Zoltán Kovács, L. Gergely

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We develop a Hamiltonian formalism of braneworld 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.

Original languageEnglish
Article number024003
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume77
Issue number2
DOIs
Publication statusPublished - Jan 7 2008

Fingerprint

Branes
scalars
projection
gravitons
Scalar
Lanczos
Projection
momentum
Momentum
heat transmission
Hamiltonian Formalism
Energy Transport
Brane World
degrees of freedom
Heat Flow
Diffeomorphism
gravitation
formalism
Curvilinear integral
decomposition

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Nuclear and High Energy Physics
  • Mathematical Physics

Cite this

Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory. / Kovács, Zoltán; Gergely, L.

In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 77, No. 2, 024003, 07.01.2008.

Research output: Contribution to journalArticle

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