Self-gravitating fundamental strings and black holes

The configuration of typical highly excited (M much greater than M-s simila r to (alpha')(-1/2)) string states is considered as the string coupling g i s adiabatically increased. The size distribution of very massive single str ing states is studied and the mass shift, due to long-range gravitational, dilatonic and axionic attraction, is estimated. By combining the two effect s, in any number of spatial dimensions d, the most probable size of a strin g state becomes of order l(s) = root 2 alpha' when g(2) M/M-s similar to 1. Depending on the dimension d, the transition between a random-walk-size st ring state (for low g) and a compact (similar to l(s)) string state(when g( 2)M/M-s similar to 1) can be very gradual (d = 3), fast but continuous (d = 4), or discontinuous (d greater than or equal to 5). Those compact string states look like nuggets of an ultradense state of string matter, with ener gy density rho similar to g(-2)M(s)(d+1). Our results extend and clarify pr evious work by Susskind, and by Horowitz and Polchinski, on the corresponde nce between self-gravitating string states and black holes. (C) 2000 Elsevi er Science B.V. All rights reserved.