Nonsingular 2-D Black Holes and Classical String Backgrounds

Abstract

We study a string-inspired classical 2-D effective field theory with {\it nonsingular} black holes as well as Witten's black hole among its static solutions. By a dimensional reduction, the static solutions are related to the $(SL(2,R)_{k}\otimes U(1))/U(1)$ coset model, or more precisely its $O\bigl((\alpha')^{0}\bigr)$ approximation known as the 3-D charged black string. The 2-D effective action possesses a propagating degree of freedom, and the dynamics are highly nontrivial. A collapsing shell is shown to bounce into another universe without creating a curvature singularity on its path, and the potential instability of the Cauchy horizon is found to be irrelevent in that some of the infalling observers never approach the Cauchy horizon. Finally a $SL(2,R)_{k}/U(1)$ nonperturbative coset metric, found and advocated by R. Dijkgraaf et.al., is shown to be nonsingular and to coincide with one of the charged spacetimes found above. Implications of all these geometries are discussed in connection with black hole evaporation.