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arXiv · 0812.4197

Wave Propagation and Scattering for the RS2 Brane Cosmology Model

Alain Bachelot
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Abstract

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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Alain Bachelot. 2009-09-21. Wave Propagation and Scattering for the RS2 Brane Cosmology Model. https://arxiv.org/abs/0812.4197

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