Statistical Mechanics on Axially-symmetric Space-times with the Killing Horizon and Entropy of Rotating Black Holes in Induced Gravity

We develop a method for computing the free-energy of a canonical ensemble of quantum fields near the horizon of a rotating black hole. We show that the density of energy levels of a quantum field on a stationary background can be related to the density of levels of the same field on a fiducial static space-time. The effect of the rotation appears in the additional interaction of the "static" field with a fiducial abelian gauge-potential. The fiducial static space-time and the gauge potential are universal, i.e., they are determined by the geometry of the given physical space-time and do not depend on the spin of the field. The reduction of the stationary axially symmetric problem to the static one leads to a considerable simplification in the study of statistical mechanics and we use it to draw a number of conclusions. First, we prove that divergences of the entropy of scalar and spinor fields at the horizon in the presence of rotation have the same form as in the static case and can be removed by renormalization of the bare black hole entropy. Second, we demonstrate that statistical-mechanical representation of the Bekenstein-Hawking entropy of a black hole in induced gravity is universal and does not depend on the rotation.Comment: 22 page

Thorny Spheres and Black Holes with Strings

We consider thorny spheres, that is 2-dimensional compact surfaces which are everywhere locally isometric to a round sphere $S^2$ except for a finite number of isolated points where they have conical singularities. We use thorny spheres to generate, from a spherically symmetric solution of the Einstein equations, new solutions which describe spacetimes pierced by an arbitrary number of infinitely thin cosmic strings radially directed. Each string produces an angle deficit proportional to its tension, while the metric outside the strings is a locally spherically symmetric solution. We prove that there can be arbitrary configurations of strings provided that the directions of the strings obey a certain equilibrium condition. In general this equilibrium condition can be written as a force-balance equation for string forces defined in a flat 3-space in which the thorny sphere is isometrically embedded, or as a constraint on the product of holonomies around strings in an alternative 3-space that is flat except for the strings. In the case of small string tensions, the constraint equation has the form of a linear relation between unit vectors directed along the string axes.Comment: 37 pages, 11 figure

Energy flux through the horizon in the black hole-domain wall systems

We study various configurations in which a domain wall (or cosmic string), described by the Nambu-Goto action, is embedded in a background space-time of a black hole in $(3+1)$ and higher dimensional models. We calculate energy fluxes through the black hole horizon. In the simplest case, when a static domain wall enters the horizon of a static black hole perperdicularly, the energy flux is zero. In more complicated situations, where parameters which describe the domain wall surface are time and position dependent, the flux is non-vanishing is principle. These results are of importance in various conventional cosmological models which accommodate the existence of domain walls and strings and also in brane world scenarios.Comment: references added, accepted for publication in JHE

Weakly magnetized black holes as particle accelerators

We study collision of particles in the vicinity of a horizon of a weakly magnetized non-rotating black hole. In the presence of the magnetic field innermost stable circular orbits (ISCO) of charged particles can be located close to the horizon. We demonstrate that for a collision of two particles, one of which is charged and revolving at ISCO and the other is neutral and falling from infinity, the maximal collision energy can be high in the limit of strong magnetic field. This effect has some similarity with the recently discussed effect of high center-of-mass energy for collision of particles in extremely rotating black holes. We also demonstrate that for `realistic' astrophysical black holes their ability to play the role of `accelerators' is in fact quite restricted.Comment: 7 pages, 5 figure

Stability and hyperfine structure of the four- and five-body muon-atomic clusters a+b+μ−e−a^{+} b^{+} \mu^{-} e^{-} and a+b+μ−e−e−a^{+} b^{+} \mu^{-} e^{-} e^{-}

Based on the results of accurate variational calculations we demonstrate stability of the five-body negatively charged ions $a^{+} b^{+} \mu^{-} e^{-} e^{-}$. Each of these five-body ions contains two electrons $e^{-}$, one negatively charged muon $\mu^{-}$ and two nuclei of the hydrogen isotopes $a, b = (p, d, t)$. The bound state properties of these five-body ions, including their hyperfine structure, are briefly discussed. We also investigate the hyperfine structure of the ground states of the four-body muonic quasi-atoms $a^{+} b^{+} \mu^{-} e^{-}$. In particular, we determine the hyperfine structure splittings for the ground state of the four-body muonic quasi-atoms: $p^{+} d^{+} \mu^{-} e^{-}$ and $p^{+} t^{+} \mu^{-} e^{-}$

Statistical Mechanics of Charged Black Holes in Induced Einstein-Maxwell Gravity

The statistical origin of the entropy of charged black holes in models of induced Einstein-Maxwell gravity is investigated. The constituents inducing the Einstein-Maxwell action are charged and interact with an external gauge potential. This new feature, however, does not change divergences of the statistical-mechanical entropy of the constituents near the horizon. It is demonstrated that the mechanism of generation of the Bekenstein-Hawking entropy in induced gravity is universal and it is basically the same for charged and neutral black holes. The concrete computations are carried out for induced Einstein-Maxwell gravity with a negative cosmological constant in three space-time dimensions.Comment: 16 pages, latex, no figure

Interaction of a brane with a moving bulk black hole

We study the interaction of an n-dimensional topological defect (n-brane) described by the Nambu-Goto action with a higher-dimensional Schwarzschild black hole moving in the bulk spacetime. We derive the general form of the perturbation equations for an n-brane in the weak field approximation and solve them analytically in the most interesting cases. We specially analyze applications to brane world models. We calculate the induced geometry on the brane generated by a moving black hole. From the point of view of a brane observer, this geometry can be obtained by solving (n+1)-dimensional Einstein's equations with a non-vanishing right hand side. We calculate the effective stress-energy tensor corresponding to this `shadow-matter'. We explicitly show that there exist regions on the brane where a brane observer sees an apparent violation of energy conditions. We also study the deflection of light propagating in the region of influence of this `shadow matter'.Comment: version accepted for publication in Phys. Rev.