Singularities and Black Holes in General Relativity

Princeton University, Princeton NJ

Investigators

Abstract

One of the most shocking predictions of general relativity is the existence of black holes; regions of spacetime so dense that nothing, not even light, can escape. In addition to possessing fascinating physical properties, black holes play an essential role in our modern understanding of astrophysics. For example, it is expected that any object undergoing gravitational collapse eventually settles down to a black hole, and also, it is thought that black holes serve to shield us from potentially dangerous gravitational singularities. However, both of these expectations, so fundamental to our view of the universe, lack a definitive mathematical understanding. This project aims to advance our understanding of both the problems of black hole stability and the potential existence of "naked singularities", singular solutions which are not hidden away behind a black hole. In the last decade there has been a tremendous progress in establishing stability results for model equations on general black hole backgrounds. At the same time, there has been much progress in understanding the true stability problem for the special class of non-rotating black holes. One part of our research plan is to combine these two research directions and to eventually establish a definitive stability theory for rotating black holes. Another part of our research plan is to show that there do in fact exist singular spacetimes which are not hidden behind black holes; however, we will also show that upon a slight perturbation, these particular spacetimes become unstable and develop a black hole. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.