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Title: Revisiting black-hole perturbation theory: the hyperboloidal slice approach

Speaker: Rodrigo Panosso Macedo (Queen Mary London)

Abstract: We present a spectral representation of solutions to relativistic wave equations
formulated on a Schwarzschild 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 grows rate. Eventually, we mention on the
extensions of the algorithm to the Reisnner-Nordstrom background and some applications on
asymptotically AdS spacetimes.