Null string evolution in black hole and cosmological spacetimes

We discuss the problem of the motion of classical strings in some black hole and cosmological spacetimes. In particular, the null string limit (zero tension) of tensile strings is considered. We present some new exact string solutions in a Reissner-Nordstr\"om black hole background as well as in the Einstein static universe and in the Einstein-Schwarzschild (a black hole in the Einstein static universe) spacetime. These solutions can give some insight into the general nature of the propagation of strings (cosmic and fundamental) in curved backgrounds.