Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime |
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Authors: | Juri Agresti Roberto De Pietri Luca Lusanna Luca Martucci |
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Affiliation: | (1) Dipartimento di Fisica, Universita' di Firenze, Polo Scientifico, via Sansone 1, 50019 Sesto Fiorentino, Italy;(2) Sezione INFN di Firenze, Polo Scientifico, via Sansone 1, 50019 Sesto Fiorentino, Italy |
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Abstract: | In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy , we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) . We define a Hamiltonian linearization of the theory, i.e. gravitational waves, withoutintroducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in . We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's , which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation. |
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Keywords: | Tetrad gravity Dirac constraints Hamiltonian Linearization |
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