A new point of view on the solutions to the Einstein constraint equations with arbitrary mean curvature and small TT-tensor

In this paper, we give a construction of the solutions to the Einstein constraint equations using the well-known conformal method. Our method gives a result similar to the one in [14, 15, 21], namely existence when the so-called TT-tensor is small and the Yamabe invariant of the manifold is positive...

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Bibliographic Details
Published in:Classical and quantum gravity 2014-10, Vol.31 (19), p.195014
Main Authors: Gicquaud, Romain, Anh Ngô, Quôc
Format: Article
Language:English
Subjects:
conformal method
Einstein constraint equations
General Relativity and Quantum Cosmology
implicit function theorem
non-CMC
Physics
positive Yamabe invariant
small TT-tensor
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Summary:In this paper, we give a construction of the solutions to the Einstein constraint equations using the well-known conformal method. Our method gives a result similar to the one in [14, 15, 21], namely existence when the so-called TT-tensor is small and the Yamabe invariant of the manifold is positive. The method we describe is, however, much simpler than the original method and allows easy extensions to several other problems. Some non-existence results are also considered.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/31/19/195014