A Striking Property of the Gravitational Hamiltonian

Details A Striking Property of the Gravitational Hamiltonian A Striking Property of the Gravitational Hamiltonian

1994-06-22

arxiv.org/abs/gr-qc/9406040v1

Phys.Rev.D50:4944-4956,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22, CGPG-94/6-3

Scientific paper

10.1103/PhysRevD.50.4944

{\sl A Hamiltonian framework for 2+1 dimensional gravity coupled with matter (satisfying positive energy conditions) is considered in the asymptotically flat context. It is shown that the total energy of the system is non-negative, vanishing if and only if space-time is (globally) Minkowskian. Furthermore, contrary to one's experience with usual field theories, the Hamiltonian is} {\rm bounded from above}. This is a genuinely non-perturbative result. {\sl In the presence of a space-like Killing field, 3+1 dimensional vacuum general relativity is equivalent to 2+1 dimensional general relativity coupled to certain matter fields. Therefore, our expression provides, in particular, a formula for energy per-unit length (along the symmetry direction) of gravitational waves with a space-like symmetry in 3+1 dimensions. A special case is that of cylindrical waves which have two hypersurface orthogonal, space-like Killing fields. In this case, our expression is related to the ``c-energy'' in a non-polynomial fashion. While in the weak field limit, the two agree, in the strong field regime they differ significantly. By construction, our expression yields the generator of the time-translation in the full theory, and therefore represents the physical energy in the gravitational field.} \footnote{$^1$}{This is a detailed account of the results presented in the Brill-Misner symposium at the University of Maryland in May1993}

Affiliated with

Also associated with

No associations

Rating

A Striking Property of the Gravitational Hamiltonian does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Striking Property of the Gravitational Hamiltonian, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Striking Property of the Gravitational Hamiltonian will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-636119