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arXiv · 1205.1377

A family of asymptotically hyperbolic manifolds with arbitrary energy-momentum vectors

Julien Cortier
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Abstract

A family of non-radial solutions of the Yamabe equation, with reference the hyperbolic space, is constructed using power series. As a result, we obtain a family of asymptotically hyperbolic metrics, with spherical conformal infinity, with scalar curvature greater than -n(n - 1), but which are a priori not complete. Moreover, any vector of R^n+1 is performed by an energy-momentun vector of one suitable metric of this family. They can in particular provide counter-examples to the positive energy-momentum theorem when one removes the completeness assumption.

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Julien Cortier. 2012-05-07. A family of asymptotically hyperbolic manifolds with arbitrary energy-momentum vectors. https://doi.org/10.1063/1.4759581

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