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

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons61165

Cortier,  Julien
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1205.1377
(Preprint), 227KB

JoMP53_102504.pdf
(Any fulltext), 151KB

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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.