Quasinormal modes and gravitational waves

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Disturbed black holes decay back to their ground state through a process known as 'quasinormal ringdown': gravitational waves are produced which exhibit both oscillatory behaviour and exponential decay, characterised by a discrete spectrum of complex numbers. With improvement in gravitational wave detectors, quasinormal ringdown is expected to be an important observational signal for gravitational wave astronomy. Recent mathematical work of Vasy and Warnick among others has provided an improved mathematical understanding of this spectrum as well as new approaches to compute the quasinormal frequencies. The goal of this project will be to adapt methods from the mathematical literature to better understand how the quasinormal spectrum of a black hole determines the geometry. One may think of this as an astrophysical version of the classical question from spectral theory: 'can you hear the shape of a drum'.