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

A family of non-radial solutions to the Yamabe equation, modeled on 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 or equal to -n(n - 1), but which are a priori not complete. Moreover, any vector of Rn+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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4759581]