Global properties of warped solutions in general relativity

Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dim ensional problem which can be solved. All global vacuum solutions are expli citly constructed and analysed. The classification of the solutions include s the Schwarzschild, the (anti-)de Sitter, and other well-known solutions b ut also many exact ones whose detailed global properties to our knowledge h ave not been discussed before. They have a natural physical interpretation describing single or several wormholes, domain walls of curvature singulari ties, cosmic strings, cosmic strings surrounded by domain walls, solutions with closed timelike curves, etc. (C) 1999 Academic Press.