EFFECTIVE ACTION AND ALL-ORDER GRAVITATIONAL EIKONAL AT PLANCKIAN ENERGIES

Building on previous work by us and by Lipatov, we present an effectiv e action approach to the resummation of all semiclassical (i.e. O(HBAR -1)) contributions to the scattering phase arising in high-energy grav itational collisions. By using an infrared-safe expression for Lipatov 's effective action, we derive an eikonal form of the scattering matri x and check that the superstring amplitude result is reproduced at fir st order in the expansion parameter R2/b2, where R, b are the gravitat ional radius and the impact parameter, respectively. If rescattering o f produced gravitons is neglected, the longitudinal coordinate depende nce can be explicitly factored out and exhibits the characteristics of a shock-wave metric while the transverse dynamics is described by a r educed two-dimensional effective action. Singular behaviours in the la tter, signalling black hole formation, can be looked for.