Applications of hidden symmetries to black hole physics

This work is a brief review of applications of hidden symmetries to black hole physics. Symmetry is one of the most important concepts of the science. In physics and mathematics the symmetry allows one to simplify a problem, and often to make it solvable. According to the Noether theorem symmetries are responsible for conservation laws. Besides evident (explicit) spacetime symmetries, responsible for conservation of energy, momentum, and angular momentum of a system, there also exist what is called hidden symmetries, which are connected with higher order in momentum integrals of motion. A remarkable fact is that black holes in four and higher dimensions always possess a set (`tower') of explicit and hidden symmetries which make the equations of motion of particles and light completely integrable. The paper gives a general review of the recently obtained results. The main focus is on understanding why at all black holes have something (symmetry) to hide.Comment: This is an extended version of the talks at NEB-14 conference (June,Ioannina,Greece) and JGRG20 meeting (September, Kyoto, Japan

Vacuum polarization of massive scalar fields in the spacetime of the electrically charged nonlinear black hole

The approximate renormalized stress-energy tensor of the quantized massive conformally coupled scalar field in the spacetime of electrically charged nonlinear black hole is constructed. It is achieved by functional differentiation of the lowest order of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficient $a_{3}.$ The result is compared with the analogous result derived for the Reissner-Nordstr\"om black hole. It is shown that the most important differences occur in the vicinity of the event horizon of the black hole near the extremality limit. The structure of the nonlinear black hole is briefly studied by means of the Lambert functions.Comment: 22 pages, 10 figure

Special Aspects of DC Air Plasma Torch’s Operating Modes under Turbulent Flow Conditions

The article is dedicated to the analysis of plasma flow turbulization processes inside DC air plasma torches. The influence of plasma torch’s arc current and plasma gas flow rate on plasma flow turbulization inside the torch channel is described. Also, measurements of voltage fluctuation due to motion of point of arc attachment are presented in the article. The mathematical model for the analysis of arc processes inside and outside of plasma torches is developed

Vacuum polarization in a cosmic string spacetime induced by flat boundary

In this paper we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated to a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary conditions on the surface orthogonal to the string.Comment: 12 pages, 5 figures, talk presented at the 8th Alexander Friedmann International Seminar on Gravitation and Cosmology, in Rio de Janeiro, Brazi