1205.1377 (Julien Cortier)

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

Julien Cortier

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. They can have an energy-momentum vector of arbitrary causal type and therefore provide counter-examples to the positive energy-momentum theorem when one removes the completeness assumption.

View original: http://arxiv.org/abs/1205.1377