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Title: Striking property of the gravitational Hamiltonian
Authors: Ashtekar, A.
Varadarajan, Madhavan
Issue Date: 1994
Publisher: American Physical Society
Citation: Physical Review D , 1994, Vol.50, p4944-4956
Abstract: 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 bounded from above. This is a genuinely nonperturbative result. In the presence of a spacelike 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 spacelike symmetry in 3+1 dimensions. A special case is that of cylindrical waves which have two hypersurface orthogonal, spacelike Killing fields. In this case, our expression is related to the ``c energy'' in a nonpolynomial 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.
Description: Restricted Access. An open-access version is available at (one of the alternative locations)
ISSN: 1550-7998
1550-2368 (0nline)
Alternative Location: 10.1103/PhysRevD.50.4944
Copyright: 1994, American Physical Society
Appears in Collections:Research Papers (TP)

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