Phase space of general relativity revisited: A canonical choice of time and simplification of the Hamiltonian

Abhay Ashtekar, Gary T. Horowitz

Research output: Contribution to journalArticle

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Abstract

The phase space of general relativity is considered in the asymptotically flat context. Using spinorial techniques introduced by Witten, a prescription is given to transport rigidly the space-time translations at infinity to the interior of the (spatial) three-manifold. This yields a preferred four-parameter family of lapses and shifts and hence reduces the infinite-dimensional freedom in the choice of "time" to the restricted freedom available in special relativity. The corresponding Hamiltonians are computed and are shown to have an especially simple form: the Hamiltonians are "diagonal" in the (spatial) derivatives of variables which define "time." Furthermore, the Hamiltonians (generating timelike translations) are shown to be positive in a neighborhood of the constraint submanifold of the phase space, even at points at which the ADM energy is negative.

Original languageEnglish (US)
Pages (from-to)1473-1480
Number of pages8
JournalJournal of Mathematical Physics
Volume25
Issue number5
DOIs
StatePublished - Jan 1 1984

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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