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De Sitter spacetime: Effects of metric perturbations on geodesic motion. (English) Zbl 1235.83039

Summary: Gravitational perturbations of the de Sitter spacetime are investigated using the Regge-Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heun-type for both electric and magnetic multipoles. The solution so obtained is used to study the deviation from an initially radial geodesic due to the perturbation. The spectral properties of the perturbed metric are also analyzed. Finally, gauge- and tetrad-invariant first-order massless perturbations of any spin are explored following the approach of Teukolsky. The existence of closed-form, i.e., Liouvillian, solutions to the radial part of the Teukolsky master equation is discussed.

MSC:

83C25 Approximation procedures, weak fields in general relativity and gravitational theory
83C10 Equations of motion in general relativity and gravitational theory
83C27 Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory
83C15 Exact solutions to problems in general relativity and gravitational theory
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