Hamiltonian theory for the axial perturbations of a dynamical spherical background
arXiv:0810.4786 · doi:10.1088/0264-9381/26/1/015003
Abstract
We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial gravitational wave in a Hamiltonian pair of variables. Then, switching to a more geometrical description of the system, we construct the only scalar combination of them. We obtain the well-known Gerlach and Sengupta scalar for axial perturbations, with no known equivalent for polar perturbations. The strategy suggested and tested here will be applied to the polar case in a separate article.
arXiv comment12 pages, accepted by Classical and Quantum Gravity
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