CURVED-SPACETIME METRIC GENERATED BY PLANCKIAN ENERGY STRING COLLISIONS

We study Planckian energy string collisions in flat spacetime as the scattering of a string in the effective curved background produced by the others as the impact parameter b decreases. We find the effective energy-density distribution sigma(rho) approximately exp {-rho2/DELTA2}, generated by these collisions. Two different regimes can be studied: intermediate impact parameters x(d) much less than b much less than square-root alpha'lns approximately-equal-to DELTA/2 (x(d) characterizing the string fluctuations) and large impact parameters b much greater than square-root alpha'lns approximately equal to DELTA/2 much greater than x(d). The effective metric generated by these collisions for large b is a gravitational shock wave of profile f(rho) approximately prho4-D, i.e., the Aichelburg-Sexl (AS) geometry for a pointlike particle of momentum p. For intermediate b, f(rho) approximately qrho2, corresponding to an extended source of momentum q. The scattering matrix in this geometry and its implications for the string collision process are analyzed. We show that the poles iGs = n, n = 0, 1, 2,..., characteristic of the scattering by the AS geometry are absent here, due to the extended nature of the effective source.