Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory
- Max-Planck-Institut fuer Radioastronomie, Auf dem Huegel 69, 53121 Bonn (Germany)
- Departments of Theoretical and Experimental Physics, University of Szeged, Dom ter 9, Szeged 6720 (Hungary)
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.
- OSTI ID:
- 21035826
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 77, Issue 2; Other Information: DOI: 10.1103/PhysRevD.77.024003; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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