Abstract

Joint work with Gustav Holzgel (Princeton University). One of the most interesting objects of general relativity are the so-called black hole spacetimes. Mathematically, they can be represented as Lorentzian manifolds possessing certain global geometrical properties and whose Lorentzian metrics satisfy a set of hyperbolic PDES (the Einstein equations). Since the Einstein equations are evolution equations, a natural question is to determine which solutions are stable or not from the point of view of the initial value problem. After an introduction to the study of the Einstein equations, I will present one particular black hole solution, namely the Schwarzschild-AdS solution, and sketch a proof of its stability for the spherically symmetric Einstein-Klein-Gordon system. If time permits, I will also discuss a linear decay result (without symmetry) on Schwarzschild-AdS and Kerr-AdS.