Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Special Relativity: Minkowski Space-Time
- Part II General Relativity: Globally Hyperbolic Einstein Space-Times
- 5 Hamiltonian Gravity in Einstein Space-Times
- 6 ADM Tetrad Gravity and Its Constraints
- 7 Post-Minkowskian and Post-Newtonian Approximations
- Part III Dirac–Bergmann Theory of Constraints
- Appendix A Canonical Realizations of Lie Algebras, Poincaré Group, Poincar´e Orbits, and Wigner Boosts
- Appendix B Grassmann Variables and Pseudo–Classical Lagrangians
- Appendix C Relativistic Perfect Fluids and Covariant Thermodynamics
- References
- Index
5 - Hamiltonian Gravity in Einstein Space-Times
from Part II - General Relativity: Globally Hyperbolic Einstein Space-Times
Published online by Cambridge University Press: 17 June 2019
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Special Relativity: Minkowski Space-Time
- Part II General Relativity: Globally Hyperbolic Einstein Space-Times
- 5 Hamiltonian Gravity in Einstein Space-Times
- 6 ADM Tetrad Gravity and Its Constraints
- 7 Post-Minkowskian and Post-Newtonian Approximations
- Part III Dirac–Bergmann Theory of Constraints
- Appendix A Canonical Realizations of Lie Algebras, Poincaré Group, Poincar´e Orbits, and Wigner Boosts
- Appendix B Grassmann Variables and Pseudo–Classical Lagrangians
- Appendix C Relativistic Perfect Fluids and Covariant Thermodynamics
- References
- Index
Summary
The following family of Einstein space-times allows the use of the 3+1 approach: (1) globally hyperbolic (this allows the ADM Hamiltonian formulation); (2) asymptotically Minkowskian at spatial infinity (all the 3-spaces approach parallel space-like hyper-planes); (3) without super-translations (at spatial infinity there is the asymptotic ADM Poincaré algebra needed for particle physics). It turns out that the asymptotic ADM Poincaré 4-momentum is orthogonal to the asymptotic hyper-planes. Therefore, the 3+1 approach allows describing the Hamiltonian formulation of metric gravity and of its first-class constraints in the family of the non-inertial rest-frames.
Keywords
- Type
- Chapter
- Information
- Non-Inertial Frames and Dirac Observables in Relativity , pp. 123 - 137Publisher: Cambridge University PressPrint publication year: 2019