In the SU(3) Einstein-Yang-Mills system sequences of static spherically symmetric regular solutions and black hole solutions exist for both the SU(2) and the SO(3) embedding. We construct the lowest regular solutions of the SO(3) embedding, missed previously, and the corresponding black holes. The SO(3) solutions are classified according to their boundary conditions and the number of nodes of the matter functions. Both, the regular and the black hole solutions are unstable.Utrecht-Preprint THU-95/8 1

SU(3) Einstein-Yang-Mills-dilaton theory possesses sequences of static spherically symmetric sphaleron and black hole solutions for the SU(2) and the SO(3) embedding. The solutions depend on the dilaton coupling constant γ, approaching the corresponding Einstein-Yang-Mills solutions for γ → 0, and Yang-Millsdilaton solutions in flat space for γ → ∞. The sequences of solutions tend to Einstein-Maxwell-dilaton solutions with different magnetic charges. The solutions satisfy analogous relations between the dilaton field and the metric for general γ. Thermodynamic properties of the black hole solutions are discussed.

Einstein-Yang-Mills-dilaton theory possesses sequences of neutral static spherically symmetric black hole solutions. The solutions depend on the dilaton coupling constant γ and on the horizon. The SU(2) solutions are labelled by the number of nodes n of the single gauge field function, whereas the SO(3) solutions are labelled by the nodes (n 1 , n 2 ) of both gauge field functions. The SO(3) solutions form sequences characterized by the node structure (j, j + n), where j is fixed. The sequences of magnetically neutral solutions tend to magnetically charged limiting solutions. For finite j the SO(3) sequences tend to magnetically charged Einstein-Yang-Mills-dilaton solutions with j nodes and charge P = √ 3. For j = 0 and j → ∞ the SO(3) sequences tend to Einstein-Maxwell-dilaton solutions with magnetic charges P = √ 3 and P = 2, respectively. The latter also represent the scaled limiting solutions of the SU(2) sequence. The convergence of the global properties of the black hole solutions, such as mass, dilaton charge and Hawking temperature, is exponential. The degree of convergence of the matter and metric functions of the black hole solutions is related to the relative location of the horizon to the nodes of the corresponding regular solutions.Preprint hep-th/9605109 Recently static black hole solutions have also been studied in Einstein-Yang-Millsdilaton (EYMD) theory [3,4,5,6,7]. SU(2) EYMD theory possesses a sequence of magnetically neutral static spherically symmetric black hole solutions, labelled by the number of nodes n of the single gauge field function. The solutions exist for arbitrary event horizon x H > 0 [3,4,5,6,7]. Here, in the limit x H → 0 regular particle-like solutions are obtained [3,4,5,8,6,7].For finite dilaton coupling constant γ, the sequence of regular neutral SU(2) EYMD solutions tends to the "extremal" EMD solution with the same dilaton coupling constant γ and with charge P = 1 for large n [4,8]. For finite event horizon x H and dilaton coupling constant γ, the corresponding sequence of neutral black hole solutions of SU(2) EYMD theory also tends to a limiting solution for large n. This limiting solution is the EMD black hole solution with the same event horizon x H , the same dilaton coupling constant γ, and with magnetic charge P = 1 [7].The magnetically neutral black hole solutions of EYMD theory have many features in common with those of Einstein-Yang-Mills (EYM) theory [9,10,11,12]. In fact, in the limit of vanishing dilaton coupling constant γ, the EYMD black hole solutions approach those of EYM theory. In SU(2) EYM theory, the limiting solutions are the RN black holes with charge P = 1 and event horizon x H , for x H > 1 [13,14,15,16]. For sequences of black holes with x H < 1 and for the regular sequence [17], the limiting solutions are different [13,14,15,16].The non-abelian SU(2) black hole solutions do not possess a global YM charge. Since they are characterized not only by their mass but in addition by an interger n, they represent (unstable [18, 19, 20, 21, 22]) counterexa...

We consider asymptotically flat static spherically symmetric black hole solutions in SU (N ) Einstein-Yang-Mills theory. Embedding the N -dimensional representation of su(2) in su(N ), the purely magnetic gauge field ansatz contains N − 1 functions. When one or more of these gauge field functions are identically zero, magnetically charged EYM black hole solutions emerge, consisting of a neutral and a charged gauge field part, based on non-abelian subalgebras and the Cartan subalgebra of su(N ), respectively. We classify these charged black hole solutions in general and present numerical solutions for SU (5) EYM theory.

SU(3) Einstein-Yang-Mills-dilaton theory possesses sequences of static spherically symmetric sphaleron and black hole solutions for the SU(2) and the SO(3) embedding. The solutions depend on the dilaton coupling constant γ, approaching the corresponding Einstein-Yang-Mills solutions for γ → 0, and Yang-Millsdilaton solutions in flat space for γ → ∞. The sequences of solutions tend to Einstein-Maxwell-dilaton solutions with different magnetic charges. The solutions satisfy analogous relations between the dilaton field and the metric for general γ. Thermodynamic properties of the black hole solutions are discussed.