The non-zero energy of 2+1 Minkowski space

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dc.creatorMarolf, Donald
dc.creatorPatiño, Leonardo
dc.date2006-04-19
dc.date2006-05-03
dc.date.accessioned2026-07-07T10:46:27Z
dc.date.available2026-07-07T10:46:27Z
dc.descriptionWe compute the energy of 2+1 Minkowski space from a covariant action principle. Using Ashtekar and Varadarajan's characterization of 2+1 asymptotic flatness, we first show that the 2+1 Einstein-Hilbert action with Gibbons-Hawking boundary term is both finite on-shell (apart from past and future boundary terms) and stationary about solutions under arbitrary smooth asymptotically flat variations of the metric. Thus, this action provides a valid variational principle and no further boundary terms are required. We then obtain the gravitational Hamiltonian by direct computation from this action. The result agrees with the Hamiltonian of Ashtekar and Varadarajan up to an overall addititve constant. This constant is such that 2+1 Minkowski space is assigned the energy E = -1/4G, while the upper bound on the energy is set to zero. Any variational principle with a boundary term built only from the extrinsic and intrinsic curvatures of the boundary is shown to lead to the same result. Interestingly, our result is not the flat-space limit of the corresponding energy -1/8G of 2+1 anti-de Sitter space.
dc.description16 pages, minor changes
dc.identifierhttps://arxiv.org/abs/hep-th/0604127
dc.identifierhttp://arxiv.org/abs/hep-th/0604127
dc.identifierPhys.Rev.D74:024009,2006
dc.identifierdoi:10.1103/PhysRevD.74.024009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183236
dc.subjectHigh Energy Physics - Theory
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleThe non-zero energy of 2+1 Minkowski space
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