Wave Propagation and Scattering for the RS2 Brane Cosmology Model

Details Wave Propagation and Scattering for the RS2 Brane Cosmology Model Wave Propagation and Scattering for the RS2 Brane Cosmology Model

2008-12-22

arxiv.org/abs/0812.4197v3

J.H.D.E. 6(4) (2009), 809-861

Physics

Mathematical Physics

3 figures

Scientific paper

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.

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