# GMR

## Seminar

### Hilbert structure on the ADM phase space

Seminar Room 1, Newton Institute

#### Abstract

The Einstein equations can be formulated as a densely defined flow on a phase space modelled on the Hilbert space H2 x H1 with appropriate decay conditions. I will show that the constraint system determines a smooth Hilbert submanifold and the ADM energy-momentum extends smoothly to the entire phase space. These constructions are motivated by the variational definition of quasi-local mass.

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