Bifurcating solutions of the Lichnerowicz equation

TL;DR

This paper thoroughly analyzes the bifurcation structure and solution count of the vacuum Lichnerowicz equation with positive cosmological constant on a specific manifold, revealing detailed properties of related CMC slicings.

Contribution

It provides a comprehensive classification of solutions and bifurcations for the Lichnerowicz equation with symmetry assumptions, extending understanding of Schwarzschild-de Sitter and Nariai spacetimes.

Findings

Detailed bifurcation diagrams for solutions

Classification of CMC slicings in Schwarzschild-de Sitter

Identification of solution multiplicities and types

Abstract

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.