Self Gravitating Fundamental Strings

TL;DR

Horowitz and Polchinski explore how a single highly excited fundamental string behaves as the string coupling increases within a black-hole/string correspondence framework. They develop and apply a thermal scalar formalism to capture free-string thermodynamics near the Hagedorn transition and extend it to include self-gravitational interactions in a mean-field treatment. They identify a dimension-dependent interplay between gravitational attraction and string tension, with a universal critical coupling $g_c \sim N^{-1/4}$ for black-hole formation and a lower threshold $g_o \sim N^{(d-6)/8}$ for interaction effects; in $d=3$ a smooth contraction to the string scale occurs before collapse, while higher dimensions show hysteresis or require dual descriptions. The results illuminate how the correspondence principle operates across dimensions and how atypical high-dimensional states reconcile black-hole entropy with long, compact strings.

Abstract

We study the configuration of a typical highly excited string as one slowly increases the string coupling. The dominant interactions are the long range dilaton and gravitational attraction. In four spacetime dimensions, the string slowly contracts from its initial (large) size until it approaches the string scale where it forms a black hole. In higher dimensions, the string stays large until the coupling reaches a critical value, and then it rapidly collapses to a black hole. The implications for the recently proposed correspondence principle are discussed.