### 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 language | English |
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Article number | 024003 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 77 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 7 2008 |

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### 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.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 77, no. 2, 024003. https://doi.org/10.1103/PhysRevD.77.024003

}

TY - JOUR

T1 - Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory

AU - Kovács, Zoltán

AU - Gergely, L.

PY - 2008/1/7

Y1 - 2008/1/7

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.77.024003

DO - 10.1103/PhysRevD.77.024003

M3 - Article

AN - SCOPUS:38049162136

VL - 77

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 2

M1 - 024003

ER -