##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Caleb Meier

#### UCSD

## Non-CMC Solutions to the Einstein Constraint Equations on Asymptotically Euclidean Manifolds

##### Abstract:

We consider the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with boundary. By leveraging both our own recent recent work as well as the work of some of our collaborators, we show that far-fromCMC and near-CMC solutions exist to the conformal formulation of the Einstein constraints when Robin-type marginally trapped surface boundary conditions are imposed to ensure that expansion scalars along null geodesics perpendicular to the boundary region are non-positive. Therefore, assuming a suitable form of weak cosmic censorship, the results we develop in this article provide a method to construct initial data that will evolve into a space-time containing an arbitrary number of black holes. A particularly important feature of our results are the minimal restrictions we place on the mean curvature, giving both near- and far-from-CMC results that are new.

### February 4, 2014

### 10:00 AM

### AP&M 2402

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