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

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

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

The near-horizon geometry of dilaton-axion black holes

Static black holes of dilaton-axion gravity become singular in the extreme limit, which prevents a direct determination of their near-horizon geometry. This is addressed by first taking the near-horizon limit of extreme rotating NUT-less black holes, and then going to the static limit. The resulting four-dimensional geometry may be lifted to a Bertotti-Robinson-like solution of six-dimensional vacuum gravity, which also gives the near-horizon geometry of extreme Kaluza-Klein black holes in five dimensions.Comment: 2 pages, "mprocl.sty" with Latex 2.09, contribution to the 9th Marcel Grossmann meeting (MG9), Rome, July 200

Electromagnetic and gravitational radiation from massless particles

We demonstrate that full description of both electromagnetic and gravitational radiation from massless particles lies outside the scope of classical theory. Synchrotron radiation from the hypothetical massless charge in quantum electrodynamics in external magnetic field has finite total power while the corresponding classical formula diverges in the massless limit. We argue that in both cases classical theory describes correctly only the low-frequency part of the spectra, while the total power diverges because of absence of the UV frequency cutoff. Failure of description of gravitational radiation from massless particles by classical General Relativity may be considered as another appeal for quantization of gravity apart from the problem of singularities.Comment: Talk given at XIIth International Conference on Gravitation, Astrophysics and Cosmology (ICGAC-12), June 28-July 5, 2015, PFUR, Moscow, Russia. To be published in the Proceedings, World Scientific, Singapor