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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 by Agresti, Juri; De Pietri, Roberto; Lusanna, Luca; Martucci, Luca is a scholarly article available to read on EtoBox.

What is 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 about?

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of {\it 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) $r_{\bar a}(\tau ,\vec \sigma)$, $\pi_{\bar a}(\tau ,\vec \sigma)$, $\bar a = 1,2$. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, {\it without introducing 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 ${\hat E}_{ADM}$. {\it 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 $r_{\bar a}(\tau ,\vec \sigma)$, which replace the two polarizations of the TT harmonic gauge, and that {\it linearized Einstein's equations are satisfied

Author

Agresti, Juri; De Pietri, Roberto; Lusanna, Luca; Martucci, Luca

Published

2003

Language

EN