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.
Circular string instabilities in curved spacetime.
We investigate the connection between curved spacetime and the emergence of string-instabilities, following the approach developed by Loustó and Sánchez for de Sitter and black hole spacetimes. We analyse the linearised equations determining the comoving physical (transverse) perturbations on circular strings embedded in Schwarzschild, Reissner-Nordström and de Sitter backgrounds. In all 3 cases we find that the " radial " perturbations grow infinitely for r → 0 (ring-collapse), while the " angular " perturbations are bounded in this limit. For r → ∞ we find that the perturbations in both physical directions (perpendicular to the string world-sheet in 4 dimensions) blow up in the case of de Sitter space. This confirms results recently obtained by Loustó and Sánchez who considered perturbations around the string center of mass.
Mechanics of stationary strings: separability of non-dispersive models in a black hole background
The problem of equilibrium in a stationary gravitational (and electromagnetic) background is formulated for a macroscopic string model of the general kind applicable to phenomena ranging from ordinary elastic strings to superconducting cosmic strings. A key role is found to be played by the tangent vector given in terms of the Killing vector and the string surface stress momentum-energy tensor. The resulting system is worked out explicitly for string models of the special non-dispersive type that has been shown to take account of the averaged effect of small-scale oscillations in a simple Goto-Nambu model, and that also arises in the more artificial case of string models obtained by dimensional reduction.