Classification of Static, Spherically Symmetric Solutions of the Einstein-Yang-Mills Theory with Positive Cosmological Constant

Abstract

We give a complete classification of all static, spherically symmetric solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological constant. Our classification proceeds in two steps. We first extend solutions of the radial field equations to their maximal interval of existence. In a second step we determine the Carter-Penrose diagrams of all 4-dimensional space-times constructible from such radial pieces. Based on numerical studies we sketch a complete phase space picture of all solutions with a regular origin.

49 pages, 19 figures, submitted to Commun. Math. Phys

Cited by in corpus (15)

• Black hole spontaneous scalarisation with a positive cosmological constant
• Classical Yang-Mills black hole hair in anti-de Sitter space
• Einstein-Yang-Mills solutions in higher dimensional de Sitter spacetime
• Existence and Newtonian limit of nonlinear bound states in the Einstein-Dirac system
• Soliton and black hole solutions of su(N) Einstein-Yang-Mills theory in anti-de Sitter space
• Skyrmion and Skyrme-Black holes in de Sitter spacetime
• On the stability of soliton and hairy black hole solutions of $\mathfrak{su}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant
• Regular solutions in $f(T)$-Yang-Mills theory
• Non-Abelian Magnetized Blackholes and Unstable Attractors
• Loop Quantum Corrected Einstein Yang-Mills Black Holes
• On the existence of topological hairy black holes in $\mathfrak{su}(N)$ EYM theory with a negative cosmological constant
• Scalar lumps with a horizon
• Euclidean solutions of Yang-Mills-dilaton theory
• Gravitating BPS Monopoles in all d=4p Spacetime Dimensions
• Nonlinear stability of the Taub-NUT soliton in 6+1 dimensions