Boundary terms and on-shell action in Ricci-based gravity theories: the Hamiltonian formulation
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909355775885312 |
|---|---|
| author | Mora-Pérez, Gerardo Olmo, Gonzalo J. Rubiera-Garcia, Diego Gómez, Diego Sáez-Chillón |
| author_facet | Mora-Pérez, Gerardo Olmo, Gonzalo J. Rubiera-Garcia, Diego Gómez, Diego Sáez-Chillón |
| contents | Considering the so-called Ricci-based gravity theories, a family of extensions of General Relativity whose action is given by a non-linear function of contractions and products of the (symmetric part of the) Ricci tensor of an independent connection, the Hamiltonian formulation of the theory is obtained. To do so, the independent connection is decomposed in two parts, one compatible with a metric tensor and the other one given by a 3-rank tensor. Subsequently, the Riemann tensor is expressed in terms of its projected components onto a hypersurface, allowing to construct the $3+1$ decomposition of the theory and the corresponding Gauss-Codazzi relations, where the boundary terms naturally arise in the gravitational action. Finally, the ADM decomposition is followed in order to construct the corresponding Hamiltonian and the ADM energy for any Ricci-based gravity theory. The formalism is applied to the simple case of Schwarzschild space-time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary terms and on-shell action in Ricci-based gravity theories: the Hamiltonian formulation Mora-Pérez, Gerardo Olmo, Gonzalo J. Rubiera-Garcia, Diego Gómez, Diego Sáez-Chillón General Relativity and Quantum Cosmology Considering the so-called Ricci-based gravity theories, a family of extensions of General Relativity whose action is given by a non-linear function of contractions and products of the (symmetric part of the) Ricci tensor of an independent connection, the Hamiltonian formulation of the theory is obtained. To do so, the independent connection is decomposed in two parts, one compatible with a metric tensor and the other one given by a 3-rank tensor. Subsequently, the Riemann tensor is expressed in terms of its projected components onto a hypersurface, allowing to construct the $3+1$ decomposition of the theory and the corresponding Gauss-Codazzi relations, where the boundary terms naturally arise in the gravitational action. Finally, the ADM decomposition is followed in order to construct the corresponding Hamiltonian and the ADM energy for any Ricci-based gravity theory. The formalism is applied to the simple case of Schwarzschild space-time. |
| title | Boundary terms and on-shell action in Ricci-based gravity theories: the Hamiltonian formulation |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2406.09526 |