Progress on Small Black Holes in String Theory

Schwarzschild black holes are classical solutions of general relativity that provide a reliable semiclassical description when their inverse temperatures, $\beta$, are much larger than the Planck length $l_p$. In weakly coupled string theory, however, a new length scale, $l_s\gg l_p$, enters, together with a maximal temperature known as the Hagedorn temperature, whose inverse, $\beta_H$, is of order $l_s$. This raises the question of what becomes of the Schwarzschild solution when $\beta$ approaches the string scale, especially in the limit $\beta \to \beta_H$.

Horowitz and Polchinski proposed that, in this regime, black holes transition into self-gravitating strings, or string stars, which can be described by an effective field theory in Euclidean spacetime. In this thesis, I review my work with collaborators on this problem. In particular, we discuss the original Horowitz--Polchinski effective field theory and its solutions, the role of higher-order corrections near six dimensions, the relation between string stars and small Euclidean black holes, and a reformulation of the problem in terms of a generalized non-abelian Thirring model. We also describe a controlled large-$k$ limit in which the dynamics simplifies, as well as extensions to non-uniform string-star solutions in the presence of a large spatial circle.