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arXiv · 0810.4786

Hamiltonian theory for the axial perturbations of a dynamical spherical background

David Brizuela·Jose M. Martin-Garcia
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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.

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David Brizuela, Jose M. Martin-Garcia. 2008-10-27. Hamiltonian theory for the axial perturbations of a dynamical spherical background. https://doi.org/10.1088/0264-9381%2F26%2F1%2F015003

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