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Journal Article

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

##### Fulltext (public)

1205.1377

(Preprint), 227KB

JoMP53_102504.pdf

(Any fulltext), 151KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Cortier, J. (2012). A family of asymptotically hyperbolic manifolds with arbitrary
energy-momentum vectors.* Journal of Mathematical Physics,* *53*(10):
102504. doi:10.1063/1.4759581.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-D25C-D

##### 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.