Oskar Schiller: The Initial Value Problem for the Generalised Einstein Equations

In this talk, I will explain that the initial value problem for the generalised Einstein equations is well-posed. In this, I adapt an approach laid out by Ringström in his book "The Cauchy Problem in General Relativity".

The generalised Einstein equations are a geometrisation of the equations of motion in the bosonic NS-NS sector of type II ten-dimensional supergravity. Hyperlocally, it can be understood as an Einstein-matter system with matter given by a two-form B and a dilaton potential \phi. I will describe how to obtain hyperlocal well-posedness for this system. I will then explain the difficulties in patching these hyperlocal developments together. If time permits, I will also give a sketch of the proof of geometric uniqueness of developments. Citing a famous Theorem from Choquet-Bruhat and Geroch, this establishes the existence of amaximal globally hyperbolic development (MGHD) for any set of initial data.