Naked singularities in four-dimensional string backgrounds

It is shown that gauged nonlinear $\sigma$ models always can be deformed by terms proportional to the field strength of the gauge fields (nonminimal gauging). These deformations can be interpreted as perturbations, by marginal operators, of conformal coset models. When applied to the $\mathrm{SL}(2, R)\times \frac{\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}{\left[\mathrm{U}\mathrm{}\right(1)\mathrm{}\times \mathrm{U}\mathrm{}(1\left)\right]}$ WZWN model, a large class of four-dimensional curved spacetime backgrounds are obtained. In particular, a naked singularity may form at a time when the volume of the Universe is different from zero.