STRING INSTABILITIES IN BLACK-HOLE SPACETIMES

We study the emergence of string instabilities in D-dimensional black hole spacetimes (Schwarzschild and Reissner-Nordstrom), and de Sitter space (in static coordinates to allow a better comparison with the bla ck hole case). We solve the first-order string fluctuations around the center-of-mass motion at spatial infinity, near the horizon, and at t he spacetime singularity. We find that the time components are always well behaved in the three regions and in the three backgrounds. The ra dial components are unstable: imaginary frequencies develop in the osc illatory modes near the horizon, and the evolution is like (tau-tau0)- P (P > 0) near the spacetime singularity r --> 0, where the world-shee t time (tau-tau0) --> 0 and the proper string length grows infinitely. In the Schwarzschild black hole, the angular components are always we ll behaved, while in the Reissner-Nordstrom case they develop instabil ities inside the horizon near r --> 0 where the repulsive effects of t he charge dominate over those attractive of the mass. In general, when ever large enough repulsive effects in the gravitational background ar e present, string instabilities develop. In de Sitter space, all the s patial components exhibit instability. The infalling of the string to the black hole singularity is like the motion of a particle in a poten tial gamma(tau-tau0)-2 where gamma depends on the D spacetime dimensio ns and string angular momentum, with gamma > 0 for Schwarzschild and g amma < 0 for Reissner-Nordstrom black holes. For (tau-tau0) --> 0 the string ends trapped by the black hole singularity.