It is shown that a generic black hole solution of the SU (2) Einstein-Yang-Mills (EYM) equations develops a new type of an infinitely oscillating behavior near the singularity. Only for certain discrete values of the event horizon radius exceptional solutions exist possessing an inner structure of the Schwarzschild or Reissner-Nordström type. 04.20.Jb, 97.60.Lf, 11.15.Kc Discovered soon after the regular Bartnik-McKinnon (BK) solutions [1], EYM black holes (BH) [2][3][4] provided new insights into the BH physics related to the no-hair and uniqueness theorems [5]. They share sphaleronic properties of the BK particle-like solutions [6] and also exhibit an unusual discreteness ('quantization' of the YM field on the event horizon) due to a singular non-linear boundary value problem in the domain between the horizon and the asymptotically flat (AF) infinity. Still, the existing knowledge of the EYM BH's (unlike the BK objects) is incomplete since only external solutions have been constructed so far (though a qualitative discussion of inner solutions is available [3]). Here we present brief results of our investigation of the interior structure of the EYM BH's which reveal new surprising features due to coupling of non-linear fields to gravity.Assume the static spherically symmetric magnetic ansatz for the YM potential(T ϕ,θ are spherical projections of the SU (2) generators) and the following parametrization of the metricwhere dΩ 2 = dθ 2 + sin 2 θdϕ 2 , and ∆, σ depend on r. The field equations include a coupled system for W , ∆where V = (W 2 − 1), F = 1 − V 2 /r 2 , and a decoupled equation for σ:These equations admit BH solutions in the domain r ≥ r h for any radius of the event horizon r h . The solutions are specified by the number n ∈ N of nodes of W thus forming a discrete set for each r h . Although it is not guaranteed a priori that the chart (1) is extendible to the full region r < r h , for AF solutions we did not meet any singularity in the interior region unless the genuine one r = 0 is reached. In terms of coordinates (1) one can find three distinct local power series solutions. The first one is Schwarzschild-like (S), it corresponds to the vacuum value of the YM field |W (0)| = 1. Using the mass function m(r), ∆ = r 2 − 2mr, one gets [3]where m 0 , b are (the only) free parameters. The second is the Reissner-Nordström (RN) type of solution which can be found assuming the leading term of ∆ to be a positive constant. This requires W (0) = W 0 = ±1, 0 and gives [3]what corresponds to the RN metric of the mass m 0 and the (magnetic) charge. The expansion contains three free parameters W 0 , m 0 , c.We have also found the third local power series solution assuming a negative value for ∆(0) (i.e. imaginary P ):Here there is only one free parameter (W 0 ) for W , ∆. The corresponding space-time near the singularity is conformal to the cylinder (after a time rescaling):However, one may suspect that such asymptotics can not correspond to a generic BH. Imposing 'boundary conditions' in the singularity we obta...

Static spherically symmetric asymptotically flat particle-like and black hole solutions are constructed within the SU(2) sector of the 4-dimensional heterotic string effective action. They separate topologically distinct Yang-Mills vacua and are qualitatively similar to the EinsteinYang-Mills sphalerons and non-abelian black holes discussed recently. New solutions possess quantized values of the dilaton charge.

The multidimensional N = 4 supersymmetric quantum mechanics (SUSY QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the considered SUSY QM both classical and quantum N = 4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. It is shown that quantum mechanical models with one quarter, one half and three quarters of unbroken(broken) supersymmetries can exist in the framework of the multidimensional N = 4 SUSY QM, while the one-dimensional N = 4 SUSY QM, constructed earlier, admits only one half or total supersymmetry breakdown. We illustrate the constructed general formalism, as well as all possible cases of the partial SUSY breaking taking as an example a direct multidimensional generalization of the one-dimensional N = 4 superconformal quantum mechanical model. Some open questions and possible applications of the constructed multidimensional N = 4 SUSY QM to the known exactly integrable systems and problems of quantum cosmology are briefly discussed. *

The dynamics of an N = 4 spinning particle in a curved background is described using the N = 4 superfield formalism. The SU(2) local ×SU(2) global N = 4 superconformal symmetry of the particle action requires the background to be a real "Kähler-like" manifold whose metric is generated by a sigma-model superpotential. The anti-de-Sitter spaces are shown to belong to this class of manifolds.

Static spherically symmetric asymptotically flat charged black hole solutions are constructed within the magnetic SU (3) sector of the 4-dimensional heterotic string effective action. They possess non-abelian hair in addition to the Coulomb magnetic field and are qualitatively similar to the Einstein-Yang-Mills colored SU (3) black holes except for the extremal case. In the extremality limit the horizon shrinks and the resulting geometry around the origin coincides with that of an extremal abelian dilatonic black hole with magnetic charge. Non-abelian hair exibits then typical sphaleron structure.