Naked singularities in low-energy, effective string theory

Abstract

Solutions to the equations of motion of the low-energy, effective field theory emerging out of compactified heterotic string theory are constructed by making use of the well known duality symmetries. Beginning with four-dimensional solutions of the Einstein massless scalar field theory in the canonical frame we first rewrite the corresponding solutions in the string frame. Thereafter, using the T- and S-duality symmetries of the low-energy string effective action we arrive at the corresponding uncharged, electrically charged and magnetically charged solutions. Brief comments on the construction of dual versions of the Kerr-Sen type using the dilatonic Kerr solution as the seed are also included. Thereafter, we verify the status of the energy conditions for the solutions in the string frame. Several of the metrics found here are shown to possess naked singularities although the energy conditions are obeyed. Dual solutions exhibit a duality in the conservation/violation of the null and averaged null energy conditions (NEC/ANEC), a fact demonstrated previously in the context of black holes (Kar S 1997 Phys. Rev. D 55 4872) and cosmologies (Kar S 1997 Phys. Lett. B 404 234). Additionally, those backgrounds which conserve the NEC/ANEC in spite of possessing naked singularities serve as counterexamples to cosmic censorship in the context of low-energy, effective string theory.