Existence Theorems for Hairy Black Holes in su(N) Einstein-Yang-Mills theories

We establish the existence of hairy black holes in su(N) Einstein-Yang-Mills theories, described by N-1 parameters, corresponding to the nodes of the gauge field functions.Comment: 64 pages, latex2e, minor changes on the nature of the parameters, version to appear in J. Math. Phy

On the Existence of Soliton and Hairy Black Hole Solutions of su(N) Einstein-Yang-Mills Theory with a Negative Cosmological Constant

We study the existence of soliton and black hole solutions of four-dimensional Einstein–Yang–Mills theory with a negative cosmological constant. We prove the existence of non-trivial solutions for any integer N, with N − 1 gauge field degrees of freedom. In particular, we prove the existence of solutions in which all the gauge field functions have no zeros. For fixed values of the parameters (at the origin or event horizon, as applicable) defining the soliton or black hole solutions, if the magnitude of the cosmological constant is sufficiently large, then the gauge field functions all have no zeros. These latter solutions are of special interest because at least some of them will be linearly stable

Infinitely Coloured Black Holes

We formulate the field equations for $SU(\infty)$ Einstein-Yang-Mills theory, and find spherically symmetric black-hole solutions. This model may be motivated by string theory considerations, given the enormous gauge symmetries which characterize string theory. The solutions simplify considerably in the presence of a negative cosmological constant, particularly for the limiting cases of a very large cosmological constant or very small gauge field. The situation of an arbitrarily small gauge field is relevant for holography and we comment on the AdS/CFT conjecture in this light. The black holes possess infinite amounts of gauge field hair, and we speculate on possible consequences of this for quantum decoherence, which, however, we do not tackle here.Comment: 23 pages latex2e, two ps figures incorporate

D-particle Recoil Space Times and "Glueball" Masses

We discuss the properties of matter in a D-dimensional anti-de-Sitter-type space time induced dynamically by the recoil of a very heavy D(irichlet)-particle defect embedded in it. The particular form of the recoil geometry, which from a world-sheet view point follows from logarithmic conformal field theory deformations of the pertinent sigma-models, results in the presence of both infrared and ultraviolet (spatial) cut-offs. These are crucial in ensuring the presence of mass gaps in scalar matter propagating in the D-particle recoil space time. The analogy of this problem with the Liouville-string approach to QCD, suggested earlier by John Ellis and one of the present authors, prompts us to identify the resulting scalar masses with those obtained in the supergravity approach based on the Maldacena's conjecture, but without the imposition of any supersymmetry in our case. Within reasonable numerical uncertainties, we observe that agreement is obtained between the two approaches for a particular value of the ratio of the two cut-offs of the recoil geometry. Notably, our approach does not suffer from the ambiguities of the supergravity approach as regards the validity of the comparison of the glueball masses computed there with those obtained in the continuum limit of lattice gauge theories.Comment: 16 pages LATEX, one LATEX figure incorporate

Monopole Black Hole Skyrmions

Charged black hole solutions with pion hair are discussed. These can be used to study monopole black hole catalysis of proton decay. There also exist multi- black hole skyrmion solutions with BPS monopole behavior.Comment: 16 pages including 6 figure

On the existence of dyons and dyonic black holes in Einstein-Yang-Mills theory

We study dyonic soliton and black hole solutions of the ${\mathfrak {su}}(2)$ Einstein-Yang-Mills equations in asymptotically anti-de Sitter space. We prove the existence of non-trivial dyonic soliton and black hole solutions in a neighbourhood of the trivial solution. For these solutions the magnetic gauge field function has no zeros and we conjecture that at least some of these non-trivial solutions will be stable. The global existence proof uses local existence results and a non-linear perturbation argument based on the (Banach space) implicit function theorem.Comment: 23 pages, 2 figures. Minor revisions; references adde

Black holes, TeV-scale gravity and the LHC

Over the past 15 years models with large extra space-time dimensions have been extensively studied. We have learned from these models that the energy scale of quantum gravity may be many orders of magnitude smaller than the conventional value of 10^19 GeV. This raises the tantalizing prospect of probing quantum gravity effects at the LHC. Of the possible quantum gravity processes at the LHC, the formation and subsequent evaporation of microscopic black holes is one of the most spectacular. We give an overview of some of the fundamental ideas of the large extra dimensions scenarios and the resulting black hole processes at the LHC