Painlevé expansions and the Einstein equations: The two-summand case

DOI10.1016/S0393-0440(03)00023-8zbMath1029.83005MaRDI QIDQ1410296

McKenzie Y. K. Wang, Andrew S. Dancer

Publication date: 14 October 2003

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

Einstein equationsgeneral relativityRicci-flat metricsPainlevé expansionsDiophantine constraints

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Equations of motion in general relativity and gravitational theory (83C10)

Cites Work

• Einstein metrics on \(S^ 3\), \(R^ 3\) and \(R^ 4\) bundles
• Existence and non-existence of homogeneous Einstein metrics
• Homogeneous Einstein metrics on spheres and projective spaces
• Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization
• On the construction of some complete metrics with exceptional holonomy
• Einstein metrics on principal fibre bundles
• Integrable cases of the Einstein equations
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. II
• The cohomogeneity one Einstein equations from the Hamiltonian viewpoint
• The cohomogeneity one Einstein equations and Painlevé analysis