Eluding the no-hair conjecture: Black holes in spontaneously broken gauge theories

Abstract

We study regular and black hole solutions to the coupled classical Einstein-Yang-MillsHiggs system. It has long been thought that black hole solutions in the spontaneously broken phase of such a theory could have no nontrivial field structure outside of the horizon. We first show that the standard black hole no-hair theorem underlying this belief, although true in the abelian setting, does not necessarily extend to the non-abelian case. This indicates the possibility of solutions with non-trivial gauge and Higgs configurations decaying exponentially outside the horizon. We then find such solutions by numerical integration of the classical equations for the case of SU(2) coupled to a Higgs doublet (the standard model less hypercharge). As a prelude to this work we also study regular and black hole solutions to Einstein-Non-Abelian-Proca theory and as a postscript we briefly discuss the important issue of stability.

Towards a novel no-hair theorem for black holes

“…On the other hand, Wheeler's hypothesis was proven wrong in e.g. Einstein-Yang-Mills [7] and Einstein-Skyrme [8] theory, in various combinations with dilaton [9] or Higgs [10] fields. Some, but not all, of these hairy black holes are unstable.…”

Black hole hair in generalized scalar-tensor gravity: An explicit example

“…The no-hair theorems inspired the development of black hole thermodynamics. However, it has been realized that hairy black holes do exist when Yang-Mills fields [10][11][12] and non-canonical scalars such as Skyrmions [13,14] are included, or when symmetries for non-gravitational fields are relaxed [15]. The possibility of having black holes with quantum hair has been discussed in Ref.…”

Stability of non-Abelian black holes and catastrophe theory

“…Besides the BM particle, researches have discovered the colored black hole [2], the Skyrmion [3,4] or the Skyrme black hole citeLM,DHS,TM, the monopole [7,8,9] or the black hole in monopole (monopole black hole) [8,9,10], the particle solution with massive Proca field (Procaon) or the Proca black hole [11], and the sphaleron citesphaleron,GMO or sphaleron black holes [11].…”