Stationary strings near a higher-dimensional rotating black hole

We study stationary string configurations in a space-time of a higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto equations for a stationary string in the 5D Myers-Perry metric allow a separation of variables. We present these equations in the first-order form and study their properties. We prove that the only stationary string configuration which crosses the infinite red-shift surface and remains regular there is a principal Killing string. A worldsheet of such a string is generated by a principal null geodesic and a timelike at infinity Killing vector field. We obtain principal Killing string solutions in the Myers-Perry metrics with an arbitrary number of dimensions. It is shown that due to the interaction of a string with a rotating black hole there is an angular momentum transfer from the black hole to the string. We calculate the rate of this transfer in a spacetime with an arbitrary number of dimensions. This effect slows down the rotation of the black hole. We discuss possible final stationary configurations of a rotating black hole interacting with a string.Comment: 13 pages, contains additianal material at the end of Section 8, also small misprints are correcte

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

Scattering of Straight Cosmic Strings by Black Holes: Weak Field Approximation

The scattering of a straight, infinitely long string moving with velocity $v$ by a black hole is considered. We analyze the weak-field case, where the impact parameter ($b_{imp}$) is large, and obtain exact solutions to the equations of motion. As a result of scattering, the string is displaced in the direction perpendicular to the velocity by an amount $\Delta b\sim -2\pi GMv\gamma/c^3 -\pi (GM)^2/ (4c^3 v b_{imp})$, where $\gamma=(1-(v/c)^2)^{-1/2}$. The second term dominates at low velocities $v/c<(GM/b_{imp})^{1/2}$ . The late-time solution is represented by a kink and anti-kink, propagating in opposite directions at the speed of light, and leaving behind them the string in a new ``phase''. The solutions are applied to the problem of string capture, and are compared to numerical results.Comment: 19 pages, 5 figure

Merger Transitions in Brane--Black-Hole Systems: Criticality, Scaling, and Self-Similarity

We propose a toy model for study merger transitions in a curved spaceime with an arbitrary number of dimensions. This model includes a bulk N-dimensional static spherically symmetric black hole and a test D-dimensional brane interacting with the black hole. The brane is asymptotically flat and allows O(D-1) group of symmetry. Such a brane--black-hole (BBH) system has two different phases. The first one is formed by solutions describing a brane crossing the horizon of the bulk black hole. In this case the internal induced geometry of the brane describes D-dimensional black hole. The other phase consists of solutions for branes which do not intersect the horizon and the induced geometry does not have a horizon. We study a critical solution at the threshold of the brane-black-hole formation, and the solutions which are close to it. In particular, we demonstrate, that there exists a striking similarity of the merger transition, during which the phase of the BBH-system is changed, both with the Choptuik critical collapse and with the merger transitions in the higher dimensional caged black-hole--black-string system.Comment: 9 pages 2 figures; additional remarks and references are added at Section IX "Discussion

Thermonuclear burn-up in deuterated methane CD4CD_4

The thermonuclear burn-up of highly compressed deuterated methane CD$_4$ is considered in the spherical geometry. The minimal required values of the burn-up parameter $x = \rho_0 \cdot r_f$ are determined for various temperatures $T$ and densities $\rho_0$. It is shown that thermonuclear burn-up in $CD_4$ becomes possible in practice if its initial density $\rho_0$ exceeds $\approx 5 \cdot 10^3$ $g \cdot cm^{-3}$. Burn-up in CD$_2$T$_2$ methane requires significantly ($\approx$ 100 times) lower compressions. The developed approach can be used in order to compute the critical burn-up parameters in an arbitrary deuterium containing fuel

Continuous Self-Similarity Breaking in Critical Collapse

This paper studies near-critical evolution of the spherically symmetric scalar field configurations close to the continuously self-similar solution. Using analytic perturbative methods, it is shown that a generic growing perturbation departs from the critical Roberts solution in a universal way. We argue that in the course of its evolution, initial continuous self-similarity of the background is broken into discrete self-similarity with echoing period $\Delta = \sqrt{2}\pi = 4.44$, reproducing the symmetries of the critical Choptuik solution.Comment: RevTeX 3.1, 28 pages, 5 figures; discussion rewritten to clarify several issue

Interaction of higher-dimensional rotating black holes with branes

We study interaction of rotating higher dimensional black holes with a brane in space-times with large extra dimensions. We demonstrate that in a general case a rotating black hole attached to a brane can loose bulk components of its angular momenta. A stationary black hole can have only those components of the angular momenta which are connected with Killing vectors generating transformations preserving a position of the brane. In a final stationary state the null Killing vector generating the black hole horizon is tangent to the brane. We discuss first the interaction of a cosmic string and a domain wall with the 4D Kerr black hole. We then prove the general result for slowly rotating higher dimensional black holes interacting with branes. The characteristic time when a rotating black hole with the gravitational radius $r_0$ reaches this final stationary state is $T\sim r_0^{p-1}/(G\sigma)$, where $G$ is the higher dimensional gravitational coupling constant, $\sigma$ is the brane tension, and $p$ is the number of extra dimensions.Comment: Version published in Class. Quant. Gra

`Thermodynamics' of Minimal Surfaces and Entropic Origin of Gravity

Deformations of minimal surfaces lying in constant time slices in static space-times are studied. An exact and universal formula for a change of the area of a minimal surface under shifts of nearby point-like particles is found. It allows one to introduce a local temperature on the surface and represent variations of its area in a thermodynamical form by assuming that the entropy in the Planck units equals the quarter of the area. These results provide a strong support to a recent hypothesis that gravity has an entropic origin, the minimal surfaces being a sort of holographic screens. The gravitational entropy also acquires a definite physical meaning related to quantum entanglement of fundamental degrees of freedom across the screen.Comment: 12 pages, 1 figur