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Well-Posedness for the Einstein Equations

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If you have a question about this talk, please contact Ciaran Hughes.

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.

This talk is part of the HEP/GR Informal Seminar Series for Graduate Students series.

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