### 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 language | English (US) |
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Pages (from-to) | 1473-1480 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 25 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 1984 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*25*(5), 1473-1480. https://doi.org/10.1063/1.526317