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Mode solutions of the Klein-Gordon equation in warped spacetimes

Philippe Droz-Vincent
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Abstract

In order to reduce the Klein-Gordon equation (with minimal coupling), we introduce a generalization of the so-called "mode solutions" that are well-known in the special case of a Robertson-Walker universe. After separation of the variables, we end up with a partial differential equation in lower dimension. A reduced version of the Gordon current arises and is conserved. When the first factor-manifold is Lorentzian, distinct modes appear as mutually orthogonal in the sense of the sesquilinear form obtained from the customary Gordon current. Moreover, a sesquilinear form is defined on the space of solutions to the reduced equation. Extension of this picture to curvature coupling is possible when the second factor-manifold has a constant scalar curvature.

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Philippe Droz-Vincent. 2000-03-31. Mode solutions of the Klein-Gordon equation in warped spacetimes. https://doi.org/10.1088/0264-9381%2F18%2F2%2F301

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