Matrix Ernst potentials for EMDA with multiple vector fields

We show that the Einstein-Maxwell-Dilaton-Axion system with multiple vector fields (bosonic sector of the D=4, N=4 supergravity) restricted to spacetimes possessing a non-null Killing vector field admits a concise representation in terms of the Ernst-type matrix valued potentials. A constructive derivation of the SWIP solutions is given and a colliding waves counterpart of the DARN-NUT solution is obtained. SU(m,m) chiral representation of the two-dimensionally reduced system is derived and the corresponding Kramer-Neugebauer-type map is presented.Comment: Latex file, no figure

Charged Stringy Black Holes With Non-Abelian Hair

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.Comment: 11 pages, LaTex, (7 figures upon request

Gravitating lumps

Recent progress in the study of solitons and black holes in non-Abelian field theories coupled to gravity is reviewed. New topics include gravitational binding of monopoles, black holes with non-trivial topology, Lue-Weinberg bifurcation, asymptotically AdS lumps, solutions to the Freedman-Schwarz model with applications to holography, non-Abelian Born-Infeld solutionsComment: A written version of the talk given at the 16th International Conference on General Relativity and Gravitation, held on July 15-21, 2001, in Durban, South Africa. Latex error on the title page corrected. New references adde

Radiation reaction in various dimensions

We discuss the radiation reaction problem for an electric charge moving in flat space-time of arbitrary dimensions. It is shown that four is the unique dimension where a local differential equation exists accounting for the radiation reaction and admitting a consistent mass-renormalization (the Dirac-Lorentz equation). In odd dimensions the Huygens principle does not hold; as a result, the radiation reaction force depends on the whole past history of a charge (radiative tail). We show that the divergence in the tail integral can be removed by the mass renormalization only in the 2+1 theory. In even dimensions higher than four, divergences can not be removed by a renormalization.Comment: Latex, 8 page

Generating solutions via sigma-models

We review recent development of solution-generating techniques for four and five-dimensional Einstein equations coupled to vector and scalar fields. This includes D=4 Einstein-Maxwell-dilaton-axion theory with multiple vector fields, D=5 Einstein-Maxwell gravity with the Chern-Simons term (minimal five-dimensional supergravity), and some other models which attracted attention in connection with black rings. The method is based on reduction to three-dimensional gravity coupled sigma-models with symmetric target spaces. Our recent results open a way to construct the general charged black rings in five-dimensional supergravity possibly coupled to vector multiplets.Comment: An updated version of the talk given at ICGA8 and published in the Proceedings. 14 pages, ptpte

Stringy Sphalerons and Non-Abelian Black Holes

Static spherically symmetric asymptotically flat particle-like and black hole solutions are constructed within the SU(2) sector of 4-dimensional heterotic string effective action. They separate topologically distinct Yang-Mills vacua and are qualitatively similar to the Einstein-Yang-Mills spha- lerons and non-abelian black holes discussed recently. New solutions possess quantized values of the dilaton charge.Comment: 12 pages, LATEX, (8 figures upon request

Quantization Near Violent Singularities in Einstein-Yang-Mills Black Holes

Classical singularities inside black holes in the Einstein-Yang-Mills theory exhibit unusual features. Only for discrete values of the black hole mass one encounters singularities of the Schwarzschild type (timelike) and the Reissner-Nordstrom type (spacelike). For a generic mass the approach to singularity is not smooth: the metric oscillates with an infinitely growing amplitude and decreasing period. In spite of some similarity with the BKL oscillations, here the behavior is not chaotic. However the oscillation amplitude exceeds classical limits after few cycles, so the question arises how this behavior gets modified by quantum effects. We discuss this issue both in the framework of QFT and in the string theory.Comment: 2 pages, Contribution to the 9th Marcel Grossmann meeting (MG9), Rome, July 200