Workshop From geometry to numerics
IHP, Paris, 20-24 November 2006

Darragh Walsh (Cork Univ., Ireland)

Non-uniqueness in conformal formulations of the Einstein Constraints

The conformal method is the simplest and most widely used method for generating solutions of Einstein's constraint equations. Numerical results by Pfeiffer and York have shown that there is a parabolic branching of solutions as initial data is varied in the extended conformal thin sandwich model. We derive identical results analytically using techniques from bifurcation theory and show that in the scalar case parabolic branching behaviour results from a poor choice of scaling that leads to linearisation instability. The implications of these results for evolution schemes will also be discussed.

[slides]

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