Strings Propagating in the 2+1 Dimensional Black Hole Anti de Sitter Spacetime

TL;DR

This paper analyzes string propagation in 2+1 dimensional black hole anti de Sitter spacetime, revealing stable oscillations, exact solutions, and the effects of rotation and different backgrounds on string behavior.

Contribution

It provides the first and second order fluctuation analysis, exact solutions for circular strings, and compares string stability across various 2+1D black hole backgrounds.

Findings

String fluctuations are stable with real frequencies.

Exact elliptic function solutions for circular string motion.

Rotation prevents strings from collapsing into the black hole.

Abstract

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.