Non-uniqueness in conformal formulations of the Einstein Constraints

  title={Non-uniqueness in conformal formulations of the Einstein Constraints},
  author={Darragh M Walsh},
Standard methods in non-linear analysis are used to indicate that there exists a parabolic branching of solutions of the LichnerowiczYork equation with an unscaled source. We also apply these methods to the extended conformal thin sandwich formulation and, by assuming that the linearised system develops a kernel solution for sufficiently large initial data, we reproduce the parabolic solution curves for the conformal factor, lapse and shift found numerically by Pfeiffer and York.