On all possible static spherically symmetric EYM solitons and black holes

Abstract

We prove local existence and uniqueness of static spherically symmetric solutions of the Einstein-Yang-Mills equations for any action of the rotation group (or SU(2)) by automorphisms of a principal bundle over space-time whose structure group is a compact semisimple Lie group G. These actions are characterized by a vector in the Cartan subalgebra of g and are called regular if the vector lies in the interior of a Weyl chamber. In the irregular cases (the majority for larger gauge groups) the boundary value problem that results for possible asymptotically flat soliton or black hole solutions is more complicated than in the previously discussed regular cases. In particular, there is no longer a gauge choice possible in general so that the Yang-Mills potential can be given by just real-valued functions. We prove the local existence of regular solutions near the singularities of the system at the center, the black hole horizon, and at infinity, establish the parameters that characterize these local solutions, and discuss the set of possible actions and the numerical methods necessary to search for global solutions. That some special global solutions exist is easily derived from the fact that su(2) is a subalgebra of any compact semisimple Lie algebra. But the set of less trivial global solutions remains to be explored.

26 pages, 2 figures, LaTeX, misprints corrected, 1 reference added

Cited by in corpus (11)

• Stationary Black Holes: Uniqueness and Beyond
• Classical Yang-Mills black hole hair in anti-de Sitter space
• Soliton and black hole solutions of su(N) Einstein-Yang-Mills theory in anti-de Sitter space
• Existence of topological hairy dyons and dyonic black holes in anti-de Sitter SU(N) Einstein-Yang-Mills theory
• Static Spherically Symmetric Solutions of the SO(5) Einstein Yang-Mills Equations
• Global behavior of solutions to the static spherically symmetric EYM equations
• Euclidean Thermodynamics and Lyapunov Exponents of Einstein-Power-Yang-Mills AdS Black Holes
• Spherical symmetry of generalized EYMH fields
• On the global existence of spherically symmetric hairy black holes and solitons in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups
• There are no magnetically charged particle-like solutions of the Einstein Yang-Mills equations for Abelian models
• On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups