Type: Article
Publication Date: 2009-12-01
Citations: 8
DOI: https://doi.org/10.1142/s0219891609002003
We study the wave equation for the gravitational waves in the Randal-Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some $L^1-L^{\infty}$, $L^2-L^{\infty}$ decay estimates and global $L^p$ Strichartz type inequalities. We develop the complete scattering theory : existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.