Strings propagating in the (2+1)-dimensional black hole anti-de Sitter spacetime.
We study the string propagation in the 2+1 black hole anti de Sitter background (2+1 BH-ADS). We find the first and second order fluctuations around the string center of mass and obtain the expression for the string mass. The string motion is stable, all fluctuations oscillate with real frequencies and are bounded, even at $r=0.$ We compare with the string motion in the ordinary black hole anti de Sitter spacetime, and in the black string background, where string instabilities develop and the fluctuations blow up at $r=0.$ We find the exact general solution for the circular string motion in all these backgrounds, it is given closely and completely in terms of elliptic functions. For the non-rotating black hole backgrounds the circular strings have a maximal bounded size $r_m,$ they contract and collapse into $r=0.$ No indefinitely growing strings, neither multi-string solutions are present in these backgrounds. In rotating spacetimes, both the 2+1 BH-ADS and the ordinary Kerr-ADS, the presence of angular momentum prevents the string from collapsing into $r=0.$ The circular string motion is also completely solved in the black hole de Sitter spacetime and in the black string background (dual of the 2+1 BH-ADS spacetime), in which expanding unbounded strings and multi-string solutions appear.
Chaotic string-capture by black hole
We consider a macroscopic charge-current carrying (cosmic) string in the background of a Schwarzschild black hole. The string is taken to be circular and is allowed to oscillate and to propagate in the direction perpendicular to its plane (that is parallel to the equatorial plane of the black hole). Numerical investigations indicate that the system is non-integrable, but the interaction with the gravitational field of the black hole still gives rise to various qualitatively simple processes like `adiabatic capture' and `string transmutation'.
A new method of near field analysis
The problem of the accurate determination of the total electromagnetic field produced by a current distribution on a circular disc type aperture is examined. For comparison of the near and Fresnel region solutions, an exact Maxwellian integral is used as the starting point. Aperture and space coordinates are separated by the use of Bessel function addition theorems, allowing the field to be expressed as a sum of terms containing radial and angular integrals. The radial integrals involve only the disc (aperture) distribution and coordinates while the angular integrals involve only the elevation angle. The distance from origin appears implicitly in the series coefficients. These integrals are suitable for high speed computations and have been evaluated for a number of cases. The results are compared with the small angle and general Fresnel formula values for various observation angles, distances from the aperture, and aperture distributions.