Linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. (English) Zbl 1311.83007
Summary: We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular, we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a nonpositive cosmological constant and of Friedman-Lemaître-Robertson-Walker spaces in a certain range of decays. We also prove that this result is no longer true for faster decays. The construction of the counterexamples is based on a new construction of transverse traceless tensors on the Euclidean space and on positive energy theorems.{
©2010 American Institute of Physics}
©2010 American Institute of Physics}
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
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