Abstract

Well-posedness is a necessary condition for any physical theory to be taken seriously, and in this talk I will review a few approaches to proving the well-posedness of the Einstein equations. First, I will briefly review well-posedness, and the centrality of “energy estimates” in its proof for wave equations. Then I will discuss the difficulties inherent in the Einstein equations, which include gauge-dependence as well as their status as a system of coupled equations. I will explain how to prove energy estimates for certain systems of equations (“symmetric-hyperbolic systems”), and then give a few ways in which the Einstein equations can be reduced to symmetric-hyperbolic form.