THE WAVE EQUATION ON SOME WARPED PRODUCT MANIFOLDS

In this study we derive solutions to the wave equation on certain types of warped product Lorentzian manifolds. We obtain solutions of the equation in the form of eigenfunctions by imposing the restriction that the solution be square integrable over the entire space-time. We show this is possible for a large class of both, warping factors and noncompact space-like manifolds. We also obtain explicit solutions, with their corresponding eigenvalues, for several of the well-known cosmological models of the universe.