Gravity seminar - Rodrigo Macedo Seminar

Abstract: After reviewing the well-established notion of black-hole perturbation
theory and the concept of quasinormal modes, we present a spectral
representation of solutions to relativistic wave equations based on a
geometrical approach in which the constant-time surfaces extend until
future null infinity. Here, we restrict ourselves to an asymptotically
flat, spherical symmetric spacetime (with focus on the
Reissner-Nordstrom solution), though the geometrical framework extends
also to the Kerr spacetime. With the help of a Laplace transformation on
the wave equation in question, we provide a geometrical interpretation
to known algorithms (i.e. Leaver’s approach) apart from deriving 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.