Time-periodic solutions of the conformally invariant wave equation on the Einstein cylinder

TL;DR

This paper investigates time-periodic solutions of the conformal wave equation on the Einstein cylinder, revealing complex bifurcation patterns through numerical and perturbative methods, as a step toward understanding Einstein equations with negative cosmological constant.

Contribution

It introduces a combined numerical and perturbative approach to identify and analyze bifurcation patterns of time-periodic solutions in the conformal wave equation on the Einstein cylinder.

Findings

Time-periodic solutions form intricate bifurcation patterns.

Numerical and perturbative techniques effectively identify solution structures.

Provides insights into the behavior of solutions relevant to Einstein equations with negative cosmological constant.

Abstract

As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative techniques, we discover that time-periodic solutions form intricate bifurcation patterns.