Self-gravitating fundamental strings and black-holes

TL;DR

This paper investigates how highly excited string states evolve under increasing gravitational coupling, revealing a transition from random-walk to compact states that resemble black hole-like objects, with the transition nature depending on spatial dimensions.

Contribution

It provides a detailed analysis of the size distribution and phase transition of self-gravitating string states, extending previous work on string-black hole correspondence across different dimensions.

Findings

Most probable string size becomes ~ l_s at g^2 M / M_s ~ 1

Transition from random-walk to compact states varies with dimension d

Compact states resemble ultradense string matter nuggets

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.