Non CMC Conformal Data Sets Which Do Not Produce Solutions of the Einstein Constraint Equations

Details Non CMC Conformal Data Sets Which Do Not Produce Solutions of the Einstein Constraint Equations Non CMC Conformal Data Sets Which Do Not Produce Solutions of the Einstein Constraint Equations

2003-11-18

arxiv.org/abs/gr-qc/0311057v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

To be published in the volume of Classical and Quantum Gravity in honour of Vincent Moncrief

Scientific paper

10.1088/0264-9381/21/3/013

The conformal formulation provides a method for constructing and parametrizing solutions of the Einstein constraint equations by mapping freely chosen sets of conformal data to solutions, provided a certain set of coupled, elliptic determined PDEs (whose expression depends on the chosen conformal data) admit a unique solution. For constant mean curvature (CMC) data, it is known in almost all cases which sets of conformal data allow these PDEs to have solutions, and which do not. For non CMC data, much less is known. Here we exhibit the first class of non CMC data for which we can prove that no solutions exist.

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