Bifurcating solutions of the Lichnerowicz equation

Piotr Chruściel (1, 2) , Romain Gicquaud (3)

1 Erwin Schrödinger Institute for Mathematical Physics
2 Faculty of Physics [Vienna]
3 LMPT - Laboratoire de Mathématiques et Physique Théorique

We give an exhaustive description of bifurcations and of the number of solutions of the vacuum Lichnerowicz equation with positive cosmological constant on $S^1\times S^2$ with $U(1)\times SO(3)$-invariant seed data. The resulting CMC slicings of Schwarzschild-de Sitter and Nariai are described.

Domains: General Relativity and Quantum Cosmology [gr-qc]; Differential Geometry [math.DG]; Analysis of PDEs [math.AP]

Piotr Chruściel, Romain Gicquaud. Bifurcating solutions of the Lichnerowicz equation. Annales Henri Poincaré, 2017, 18 (2), pp.643-679. ⟨10.1007/s00023-016-0501-x⟩. ⟨hal-01160781⟩