Behaviour of Waves on Higher Dimensional Black Hole Spacetimes

The concept of a black hole is one of the most fascinating predictions of Einstein's Theory of General Relativity. Understanding the stability properties of theses objects from a rigorous mathematical point of view is crucial for our interpretation of both Einstein's theory and of astrophysical observations.

New mathematical techniques in the study Partial Differential Equations have been developed in the past 10-15 years to address the difficult problem of stability of black holes. At the center of these developments is a mathematically robust framework to understand wave propagation on black hole spacetimes.

The aims and objectives of the research project are to investigate which of these new techniques can be applied to the study of higher dimensional black hole spacetimes. (The latter exhibit more complicated spacetime geometries and are widely studied in theoretical physics, the main example being the so-called black ring.) It is known that not all of the techniques carry through directly, so new methods in PDE analysis will have to be developed by the student to prove theorems regarding the global behaviour of waves on these spacetimes. Besides applications in theoretical physics (where various instabilities are being conjectured) this will further elucidate the intricate relationship between spacetime geometry and the dispersion of waves.