Self-gravitating fundamental strings and black holes Original Research Article

The configuration of typical highly excited (M≫Ms∼(α′)−1/2) string states is considered as the string coupling g is adiabatically increased. The size distribution of very massive single string states is studied and the mass shift, due to long-range gravitational, dilatonic and axionic attraction, is estimated. By combining the two effects, in any number of spatial dimensions d, the most probable size of a string state becomes of order ℓs=2 α′ when g2M/Ms∼1. Depending on the dimension d, the transition between a random-walk-size string state (for low g) and a compact (∼ℓs) string state (when g2M/Ms∼1) can be very gradual (d=3), fast but continuous (d=4), or discontinuous (d⩾5). Those compact string states look like nuggets of an ultradense state of string matter, with energy density ρ∼g−2Msd+1. Our results extend and clarify previous work by Susskind, and by Horowitz and Polchinski, on the correspondence between self-gravitating string states and black holes.