Global Results for Linear Waves on Expanding Kerr and Schwarzschild de Sitter Cosmologies
Communications in Mathematical Physics | Springer (part of Springer Nature) | Published : 2015
In this global study of solutions to the linear wave equation on Schwarzschild de Sitter spacetimes we attend to the cosmological region of spacetime which is bounded in the past by cosmological horizons and to the future by a spacelike hypersurface at infinity. We prove an energy estimate capturing the expansion of that region, which combined with earlier results for the static region, yields a global boundedness result for linear waves. It asserts that a general finite energy solution to the global initial value problem has a limit on the future boundary at infinity that can be viewed as a function on the standard cylinder with finite energy, and that, moreover, any decay along the cosmolo..View full abstract
This paper has grown out of work that I completed in significant parts in my thesis. I would like to thank foremost my advisor Mihalis Dafermos for many insightful discussions and for suggesting this problem to me. I am very grateful for his support during my Ph.D. and beyond. I have also benefited greatly from conversations with Willie Wong during his time at Cambridge, and more recently at MSRI. The author thanks the Engineering Physical Sciences Research Council (UK), the Cambridge European Trust and the European Research Council for their financial support during his graduate studies, and the National Science Foundation (US) for their support of postdoctoral research at MSRI.