STRINGS FALLING INTO SPACETIME SINGULARITIES

We study the dynamics of strings near spacetime singularities. We consider gravitational-wave backgrounds with a singularity of the type \U\-beta, U being a null coordinate. [The case with a delta(U) shock-wave singularity turns out to be similar to the beta = 1 case.] New features in the string behavior appear: when beta greater-than-or-equal-to 2, the string does not propagate through the gravitational wave and it escapes to infinity grazing the singularity plane U = 0; one transverse coordinate does not oscillate in time (neither classically nor quantum mechanically) and the tunnel effect does not take place. The expectation value of the mass squared <M > 2> and mode number <N >> operators and of the energy-momentum tensor are computed. When the transverse size (rho-0) of the gravitational-wave front is infinite, divergences in <M > 2> and <N >> appear for 1 less-than-or-equal-to beta < 2 and 3/2 less-than-or-equal-to beta < 2, respectively. We argue that the short-distance spacetime singularity at U = 0 is not responsible for these divergences, but the infinite amount of energy carried by the gravitational wave when rho-0 = infinity. In summary, the propagation of strings through these singular spacetimes is proven to be physically meaningful for beta greater-than-or-equal-to 2 and beta < 1. We conjecture that this is also the case for 1 less-than-or-equal-to beta < 2.