Seminar of the Institute
Wave equations in curved backgrounds: numerical applications to black-hole quasi-normal modes and AdS/CFT correspondence
Wednesday October 26, 2016 16:15:00 CEST
Wednesday October 26, 2016 17:15:00 CEST
Rodrigo Panosso Macedo (FSU Jena)
Abstract: We present a spectral representation of solutions to relativistic wave equations formulated on a Schwarzschild-black-hole background. We first consider an asymptotically flat spacetime and, after performing a Laplace transformation on the wave equation in question, we present an algorithm for obtaining all ingredients of the desired spectral decomposition, including quasi-normal modes, quasi-normal mode amplitudes as well as the jump of the Laplace-transform along the branch cut. The work explains extensively this procedure and includes detailed discussions of relevant aspects, such as the contribution of infinity frequencies modes to the early time response of the black hole and its relation to the QNM-amplitudes grow’s rate. In a second part, we employ the same strategy to study the solution of wave equations on an asymptotically AdS background. The system models the response of the chiral magnetic effect due to continuous quenches induced by time dependent electric fields via AdS/CFT correspondence and here, we focus on the possibility of considering the asymptotic growth rate of the amplitudes as a well defined notion of initial time scale for linearized systems.