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.
Two-dimensional algebraic-geometric operators with self-consistent potentials
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Separability of string equilibrium equations in a generalised Kerr-de Sitter background
The equilibrium conditions for a cosmic string in a stationary asymptotically flat Kerr black hole background have been shown to be separable. It is shown that the algebraic conditions for the background metric to allow such separability are more restrictive than those required merely for simple geodesic Hamilton-Jacobi separability. However they are not more severe than, but just equivalent to, those required for separation of the scalar wave equation as well, for which the corresponding vacuum solutions of the Einstein-Maxwell equations with the cosmological Lambda term have turned out to satisfy even more restrictive conditions giving higher spin separability. This class of solutions in which the string equilibrium equations are thus automatically separable (in the rest frame of the primary Killing vector) includes members interpretable as representing equilibrium states of a rotating black hole in an asymptotically de Sitter background.