Speaker: Benjamin Withers
Mode completeness for black hole perturbations
For approximately 40 years the state of the art in black hole spectroscopy has been to try to represent retarded Green’s functions as a sum of quasinormal modes. This appears to follow as a natural consequence from doing a Fourier integral. However, it is well known that such a sum cannot be complete, and at early times the quasinormal mode sum does not converge. I will present a resolution of this puzzle, and show that retarded Green’s functions of black hole spacetimes can be expressed as a convergent mode sum everywhere in spacetime. At late times a quasinormal mode sum converges, while at early times a Matsubara mode sum converges. The two regions are separated by a lightcone which scatters from the black hole potential. This provides a complete framework for black hole perturbations, with applications to gravitational waveform modelling or real-time quantum dynamics via AdS/CFT.