Self-gravitating fundamental strings and black-holes

TL;DR

This work investigates self-gravitating, highly excited string states across spatial dimensions to illuminate the string–black hole correspondence. By combining a microcanonical/grand canonical treatment of string oscillators with a semi-classical mass-shift calculation from long-range field exchanges, the authors derive the entropy S(M,R) and identify the most probable string size R*(M,g) as a function of dimension. They find that the transition from a random-walk, diffuse string state to a compact, dense configuration occurs smoothly for d≤4 but can be discontinuous for d≥5, with a dense $\rho\sim g^{-2}$ state that can resemble a black hole and signals a dimension-dependent crossover to a BH-like regime. These results support a continuous, physically transparent string–black hole correspondence, clarify the role of dimensionality in the transition, and offer a plausible endpoint scenario for black hole evaporation in string theory.

Abstract

The configuration of typical highly excited (M >> M_s ~ (alpha')^{-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 l_s = sqrt{2 alpha'} when g^2 M / M_s ~ 1. Depending on the dimension d, the transition between a random-walk-size string state (for low g) and a compact (~ l_s) string state (when g^2 M / M_s ~ 1) can be very gradual (d=3), fast but continuous (d=4), or discontinuous (d > 4). Those compact string states look like nuggets of an ultradense state of string matter, with energy density rho ~ g^{-2} M_s^{d+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.