## On the structure of solutions to the static vacuum Einstein equations.(English)Zbl 0981.83013

The author considers the geometry of 3-manifold solutions $$(M,g,u)$$ of type $$(0,1)$$ (i.e. the space-like hypersurfaces) to study the mathematical aspects of the equations (e.g. Einstein vacuum equations) and their solutions including those which might not be relevant physically, for example, a solution with negative mass is also allowed here.

### MSC:

 83C15 Exact solutions to problems in general relativity and gravitational theory 83C40 Gravitational energy and conservation laws; groups of motions

### Keywords:

static vacuum; Einstein vacuum equations; negative mass
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