On Spherically Symmetric String Solutions in Four Dimensions

TL;DR

This paper derives the most general spherically symmetric, asymptotically flat, and static solutions to low-energy string equations in four dimensions, incorporating various fields and symmetries, and relaxing previous singularity constraints.

Contribution

It introduces a comprehensive algebraic method to construct general solutions with multiple fields and charges, expanding beyond previous restrictions on singularities and specific backgrounds.

Findings

Constructed the general solution from a simple seed using SL(2,R) and O(1,1) symmetries.

Included general background fields: metric, dilaton, axion, and gauge fields.

Identified solution parameters with physical charges and asymptotic behaviors.

Abstract

We reconsider here the problem of finding the general 4D spherically symmetric, asymptotically flat and time-independent solutions to the lowest-order string equations in the $\ap$ expansion. Our construction includes earlier work, but differs from it in three ways. (1) We work with general background metric, dilaton, axion and $U(1)$ gauge fields. (2) Much of the original solutions were required to be nonsingular at the apparent horizon, motivated by an interest in finding string corrections to black hole spacetimes. We relax this condition throughout, motivated by the realization that string theory has a less restrictive notion of what constitutes a singular field configuration than do point particle theories. (3) We can construct the general solution from a particularly simple one, by generating it from successive applications of the {\it noncommuting} \sltwor\ and \ooneone\ symmetries of the low-energy string equations containing $S$ and target--space dualities respectively. This allows its construction using relatively simple, purely algebraic, techniques. The general solution is determined by the asymptotic behaviour of the various fields: \ie\ by the mass, dilaton charge, axion charge, electric charge, magnetic charge, and Taub-NUT parameter.