STATIONARY STRINGS AND 2-D BLACK HOLES

A general description of string excitations in stationary spacetimes is developed. If a stationary string passes through the ergosphere of a 4-dimensional black hole, its world-sheet describes a 2-dimensional black (or white) hole with horizon coinciding with the static limit of the 4-dimensional black hole. Mathematical results for 2-dimensional black holes can therefore be applied to physical objects (say) cosmic strings in the vicinity of Kerr black holes. An immediate general result is that the string modes are thermally excited. The string excitations are determined by a coupled system of scalar field equations in the world-sheet metric. In the special case of excitations propagating along a stationary string in the equatorial plane of the Kerr-Newman black hole, they reduce to the $s$-wave scalar field equations in the 4-dimensional Reissner-Nordstr\"{o}m black hole. We briefly discuss possible applications of our results to the black hole information puzzle.