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Electromagnetic and Gravitational Waves on a de Sitter background | Roberto Valentino Montaquila
; | Date: |
16 Apr 2010 | Abstract: | One of the longstanding problems of modern gravitational physics is the
detection of gravitational waves, for which the standard theoretical analysis
relies upon the split of the space-time metric into a background metric plus
perturbation. However, as is well known, the background need not be Minkowskian
in several cases of physical interest. Thus, we here investigate in more detail
what happens if the background space-time has a non-vanishing Riemann
curvature. In the case in which the de Donder gauge is imposed, its
preservation under infinitesimal space-time diffeomorphisms is guaranteed if
and only if the associated covector is ruled by a second-order hyperbolic
operator. Moreover, since in this case the Ricci term of the wave equation has
opposite sign with respect to the wave equation of Maxwell theory in the Lorenz
gauge, it is possible to relate the solutions of the two problems. We solve
completely the homogeneous vector wave equation of Maxwell theory in the Lorenz
gauge when a de Sitter space-time is considered. The decoupling technique,
analytic formulae and plots are original and have been first presented, in the
literature, by Bini, Esposito and the author in Gen. Rel. Grav. 42, 51-61
(2010). Moreover, we solve explicitly the Einstein equations for metric
perturbations on a de Sitter background. In fact, by using the Regge-Wheeler
gauge, the coupled system of differential equations, to first-order in the
metric perturbation, has been here solved in terms of the Heun general
functions. | Source: | arXiv, 1004.2805 | Services: | Forum | Review | PDF | Favorites |
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