QUANTUM STRING THEORY IN CURVED SPACE-TIMES

A general method to quantize strings in curved space‐times is exposed. It treats the space‐time metric exactly and the string excitations small as compared with the energy scale of the geometry. The method is applied to cosmological (de Sitter) and black‐hole (Schwarzschild) geometries. The critical dimension decreases in one for de Sitter and stays unaltered for black‐holes as compared with flat space‐time values. Bogoliubov transformations in the context of string theory are derived and the Bogoliubov coefficients describing elastic and inelastic scattering and excitation of modes are computed explicitely. The string‐black‐hole cross section is derived and a pair mode creation phenomena is found. The quantization and scattering of strings in shockwave geometries (ultrarelativistic boosted black‐holes or Aichelburg‐Sexl space time) is found to be exactly solvable. Copyright © 1990 WILEY‐VCH Verlag GmbH & Co. KGaA